Tbilisi Mathematical Journal Articles (Project Euclid)
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The latest articles from Tbilisi Mathematical Journal on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2018 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Fri, 20 Apr 2018 09:47 EDTFri, 20 Apr 2018 09:47 EDThttps://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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Wreaths, mixed wreaths and twisted coactions
https://projecteuclid.org/euclid.tbilisi/1524232072
<strong>Ross Street</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 10, Number 3, 1--22.</p><p><strong>Abstract:</strong><br/>
Distributive laws between two monads in a 2-category $\mathscr K$, as defined by Jon Beck in the case $\mathscr{K} = \mathrm{Cat}$, were pointed out by the author to be monads in a 2-category $\mathrm{Mnd}\mathscr{K}$ of monads. Steve Lack and the author defined wreaths to be monads in a 2-category $\mathrm{EM}\mathscr{K}$ of monads with different 2-cells from $\mathrm{Mnd}\mathscr{K}$.
Mixed distributive laws were also considered by Jon Beck, Mike Barr and, later, various others; they are comonads in $\mathrm{Mnd}\mathscr{K}$. Actually, as pointed out by John Power and Hiroshi Watanabe, there are a number of dual possibilities for mixed distributive laws.
It is natural then to consider mixed wreaths as we do in this article; they are comonads in $\mathrm{EM}\mathscr{K}$. There are also mixed opwreaths: comonads in the Kleisli construction completion $\mathrm{Kl}\mathscr{K}$ of $\mathscr{K}$. The main example studied here arises from a twisted coaction of a bimonoid on a monoid. A wreath determines a monad structure on the composite of the two endomorphisms involved; this monad is called the wreath product. For mixed wreaths, corresponding to this wreath product, is a convolution operation analogous to the convolution monoid structure on the set of morphisms from a comonoid to a monoid. In fact, wreath convolution is composition in a Kleisli-like construction. Walter Moreira’s Heisenberg product of linear endomorphisms on a Hopf algebra, is an example of such convolution, actually involving merely a mixed distributive law. Monoidality of the Kleisli-like construction is also discussed.
</p>projecteuclid.org/euclid.tbilisi/1524232072_20180420094755Fri, 20 Apr 2018 09:47 EDTA note to establish the Hyers-Ulam stability for a nonlinear integral equation with Lipschitzian kernelhttps://projecteuclid.org/euclid.tbilisi/1538532025<strong>Mohammad Saeed Khan</strong>, <strong>Dinu Teodorescu</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 3, 41--45.</p><p><strong>Abstract:</strong><br/>
In the stability theory, the nonlinear equations were not so much investigated. In this note we consider the stability of a nonlinear integral equation with Lipschitzian kernel. The approach is based on monotonicity properties of a nonlinear operator.
</p>projecteuclid.org/euclid.tbilisi/1538532025_20181002220035Tue, 02 Oct 2018 22:00 EDTThe transmuted Gompertz-G family of distributions: properties and applicationshttps://projecteuclid.org/euclid.tbilisi/1538532026<strong>Hesham Reyad</strong>, <strong>Farrukh Jamal</strong>, <strong>Soha Othman</strong>, <strong>G. G. Hamedani</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 3, 47--67.</p><p><strong>Abstract:</strong><br/>
We introduce and study a new class of continuous distributions called the transmuted Gompertz-G family which extends the Gompertz class proposed by Alizadeh et al. (2016a). Explicit expressions for the ordinary and incomplete moments, generating function, probability weighted moment, Lorenz and Bonferroni curves, order statistics, Rényi and Shanon entropies, stress strength model moment of residual and reversed residual life and characterizations for the new family are investigated. We discuss the maximum likelihood estimates for the model parameters. The performance of the new family is assesed by means of two applications.
</p>projecteuclid.org/euclid.tbilisi/1538532026_20181002220035Tue, 02 Oct 2018 22:00 EDTA nilpotent Whitehead theorem for $\mathsf{TQ}$-homology of structured ring spectrahttps://projecteuclid.org/euclid.tbilisi/1538532027<strong>Michael Ching</strong>, <strong>John E. Harper</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 3, 69--79.</p><p><strong>Abstract:</strong><br/>
The aim of this short paper is to prove a $\mathsf{TQ}$-Whitehead theorem for nilpotent structured ring spectra. We work in the framework of symmetric spectra and algebras over operads in modules over a commutative ring spectrum. Our main result can be thought of as a $\mathsf{TQ}$-homology analog for structured ring spectra of Dror's generalized Whitehead theorem for topological spaces; here $\mathsf{TQ}$-homology is short for topological Quillen homology. We also prove retract theorems for the $\mathsf{TQ}$-completion and homotopy completion of nilpotent structured ring spectra.
</p>projecteuclid.org/euclid.tbilisi/1538532027_20181002220035Tue, 02 Oct 2018 22:00 EDTConnection problems and matrix representations for certain hybrid polynomialshttps://projecteuclid.org/euclid.tbilisi/1538532028<strong>Subuhi Khan</strong>, <strong>Tabinda Nahid</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 3, 81--93.</p><p><strong>Abstract:</strong><br/>
In this paper, we deal with the connection and duplication problems associated with the hybrid Sheffer family. The hybrid Sheffer polynomials are also studied via matrix approach. The properties of these polynomials are established using simple matrix operations. Examples providing the corresponding results for certain members of the hybrid Sheffer family are considered. This article is first attempt in the direction of obtaining connection and duplication coefficients and matrix representations for the hybrid polynomials.
</p>projecteuclid.org/euclid.tbilisi/1538532028_20181002220035Tue, 02 Oct 2018 22:00 EDTLogarithmic-Sheffer polynomials of the second kindhttps://projecteuclid.org/euclid.tbilisi/1538532029<strong>Paolo Emilio Ricci</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 3, 95--106.</p><p><strong>Abstract:</strong><br/>
In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers, and several integer sequences related to them have been studied. In this article new sets of logarithmic-Sheffer polynomials are introduced. Connection with Bell numbers are shown.
</p>projecteuclid.org/euclid.tbilisi/1538532029_20181002220035Tue, 02 Oct 2018 22:00 EDTCommon fixed points of set mappings endowed with directed graphshttps://projecteuclid.org/euclid.tbilisi/1538532030<strong>Jamshaid Ahmad</strong>, <strong>Ahmed Al-Rawashdeh</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 3, 107--123.</p><p><strong>Abstract:</strong><br/>
The aim of this article is to obtain common fixed points of set mappings defined on a family of sets endowed with a graph satisfying $\Theta-$contraction. Our results generalize and extend various results in the existing literature. We also provide some non trivial examples to support the validity of our main results. Some applications to the construction of common fixed points of set mappings in $\varepsilon$-chainable metric space are also discussed.
</p>projecteuclid.org/euclid.tbilisi/1538532030_20181002220035Tue, 02 Oct 2018 22:00 EDTCertain results on para-Kenmotsu manifolds equipped with $M$-projective curvature tensorhttps://projecteuclid.org/euclid.tbilisi/1538532031<strong>Abhishek Singh</strong>, <strong>Shyam Kishor</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 3, 125--132.</p><p><strong>Abstract:</strong><br/>
The purpose of the article is to study the certain results on para-Kenmotsu manifolds equipped with $M$-projective curvature tensor. Here we investigate para-Kenmotsu manifolds satisfying some curvature conditions $\widetilde{M}\cdot R=0,$ $\widetilde{M}\cdot Q=0$ and $Q\cdot \widetilde{M}=0,$ where $R$, $Q$ and $\widetilde{M}$ respectively denote the Riemannian curvature tensor, Ricci operator and $M$-projective curvature tensor.
</p>projecteuclid.org/euclid.tbilisi/1538532031_20181002220035Tue, 02 Oct 2018 22:00 EDTMarcinkiewicz integrals with rough kernel associated with Schrödinger operators and commutators on generalized vanishing local Morrey spaceshttps://projecteuclid.org/euclid.tbilisi/1538532032<strong>Ferit Gürbüz</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 3, 133--156.</p><p><strong>Abstract:</strong><br/>
Let $L=-\Delta+V\left( x\right) $ be a Schrödinger operator, where $\Delta$ is the Laplacian on ${\mathbb{R}^{n}}$, while nonnegative potential $V\left(x\right)$ belonging to the reverse Hölder class. In this paper, using the some conditions on $\varphi\left(x.r\right) $, we dwell on the boundedness of Marcinkiewicz integrals with rough kernel associated with schrödinger operators and commutators generated by these operators and local Campanato functions both on generalized local Morrey spaces and on generalized vanishing local Morrey spaces, respectively. As an application of the above results, the boundedness of parametric Marcinkiewicz integral and its commutator both on generalized local Morrey spaces and on generalized vanishing local Morrey spaces is also obtained.
</p>projecteuclid.org/euclid.tbilisi/1538532032_20181002220035Tue, 02 Oct 2018 22:00 EDTMultiple solutions of critical singular degenerate elliptic system with concave-convex nonlinearitieshttps://projecteuclid.org/euclid.tbilisi/1538532033<strong>Chang-Mu Chu</strong>, <strong>Lin Li</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 3, 157--174.</p><p><strong>Abstract:</strong><br/>
This paper is devoted to study a class of critical singular degenerate elliptic system with concave-convex nonlinearities and sign-changing weight functions. The existence and multiplicity of nontrivial nonnegative solutions are obtained by the variational.
</p>projecteuclid.org/euclid.tbilisi/1538532033_20181002220035Tue, 02 Oct 2018 22:00 EDTSome estimations of summation-integral-type operatorshttps://projecteuclid.org/euclid.tbilisi/1538532034<strong>Vishnu Narayan Mishra</strong>, <strong>Rishikesh Yadav</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 3, 175--191.</p><p><strong>Abstract:</strong><br/>
In this paper, the Szász-Mirakjan-Kantorovich type operators are studied with the help of direct result and weighted approximation properties. Some basic lemmas, theorems are given and proved, at last, we discuss the rate of convergence and a comparison takes place with the Szász-Mirakjan-Kantorovich operators by graphical representations.
</p>projecteuclid.org/euclid.tbilisi/1538532034_20181002220035Tue, 02 Oct 2018 22:00 EDTDouble absolute indexed matrix summability with its applicationshttps://projecteuclid.org/euclid.tbilisi/1546570881<strong>B. B. Jena</strong>, <strong>S. K. Paikray</strong>, <strong>U. K. Misra</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 4, 1--18.</p><p><strong>Abstract:</strong><br/>
The well established theory of summability of simple series has been brought to a high degree of development; however the extension of this theory to multiple series is still in its infancy. As regards to the double series, in the proposed paper a result on absolute indexed matrix summability with an additional parameter of doubly infinite lower triangular matrix has been established that generalizes a theorem of E. Savaş and B. E. Rhoades [10] (see E. Savaş and B. E. Rhoades, Double absolute summability factor theorems and applications, Nonlinear Anal. 69 (2008), 189-200). Furthermore, some concluding remarks and applications are presented in support of our result.
</p>projecteuclid.org/euclid.tbilisi/1546570881_20190103220131Thu, 03 Jan 2019 22:01 ESTSemi-slant Riemannian maps from almost contact metric manifolds into Riemannian manifoldshttps://projecteuclid.org/euclid.tbilisi/1546570882<strong>Rajendra Prasad</strong>, <strong>Sushil Kumar</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 4, 19--34.</p><p><strong>Abstract:</strong><br/>
Firstly, a generalization of Riemannian submersions, slant submersions and semi-slant submersions, we introduce semi-slant Riemannian maps from almost contact metric manifolds onto Riemannian manifolds. In this paper, we obtain some results on such maps by taking the vertical structure vector field. Among them, we study integrability of distributions and the geometry of foliations. Further, we find the necessary and sufficient conditions for semi-slant Riemannian maps to be harmonic and totally geodesic. We, also investigate some decomposition theorems and provide some examples to show the existence of the maps.
</p>projecteuclid.org/euclid.tbilisi/1546570882_20190103220131Thu, 03 Jan 2019 22:01 ESTNon-global solutions for a class of fourth-order wave equationshttps://projecteuclid.org/euclid.tbilisi/1546570883<strong>Tarek Saanouni</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 4, 35--42.</p><p><strong>Abstract:</strong><br/>
Adopting the so-called concavity method, we establish a finite time blow-up result for a class of fourth-order non-linear wave equations with positive energy.
</p>projecteuclid.org/euclid.tbilisi/1546570883_20190103220131Thu, 03 Jan 2019 22:01 ESTA note on the new set operator $\psi_{r}$https://projecteuclid.org/euclid.tbilisi/1546570884<strong>Arife Atay</strong>, <strong>Hasan İlhan Tutalar</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 4, 43--52.</p><p><strong>Abstract:</strong><br/>
Recently many published works made on local function used in ideal topological spaces can be found in related literature. "Semi Local Functions in Ideal Topological Spaces", "Closure Local Functions", and "$()^p$ and $\psi_p$-Operator" can be mentioned among such works those aim to define such functions. In general, the researchers prefer using the generalized open sets instead of topology in ideal topological spaces. Obtaining a Kuratowski closure operator with the help of local functions is an important detail in ideal topological space. However, it is not possible to obtain a Kuratowski closure operator from many of these local functions proposed by the above mentioned works. In order to address the lack of such an operator, the goal of this paper is to introduce another local function to give possibility of obtaining a Kuratowski closure operator. On the other hand, regular local functions defined for ideal topological spaces have not been found in the current literature. Regular local functions for the ideal topological spaces has been described within this work. Moreover, with the help of regular local functions Kuratowski closure operators $cl_I^{*r}$ and $\tau^{*r}$ topology are obtained. Many theorems in the literature have been revised according to the definition of regular local functions.
</p>projecteuclid.org/euclid.tbilisi/1546570884_20190103220131Thu, 03 Jan 2019 22:01 ESTModified Apostol-Euler numbers and polynomials of higher orderhttps://projecteuclid.org/euclid.tbilisi/1546570885<strong>Maged G. Bin-Saad</strong>, <strong>Ali Z. Bin-Alhag</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 4, 53--66.</p><p><strong>Abstract:</strong><br/>
The purpose of this work is to give modified definitions of Apostol-Euler polynomials and numbers of higher order. We establish their elementary properties, sums, explicit relations, integrals and differential relations. A number of new results which introduced are generalization of known results and their special cases lead to the corresponding formulas of the classical Euler numbers and polynomials.
</p>projecteuclid.org/euclid.tbilisi/1546570885_20190103220131Thu, 03 Jan 2019 22:01 ESTUniqueness results related to L-functions and certain differential polynomialshttps://projecteuclid.org/euclid.tbilisi/1546570886<strong>Pulak Sahoo</strong>, <strong>Samar Halder</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 4, 67--78.</p><p><strong>Abstract:</strong><br/>
In this paper, using the idea of weighted sharing we investigate the uniqueness problem of a meromorphic function and an $L$-function when certain differential polynomials generated by them share a nonzero finite value or have the same fixed points. Our results improve the recent results due to Liu-Li-Yi [Proc. Japan Acad. Ser. A, 93 (2017), 41-46].
</p>projecteuclid.org/euclid.tbilisi/1546570886_20190103220131Thu, 03 Jan 2019 22:01 ESTBlending type approximation by Stancu-Kantorovich operators associated with the inverse Pólya-Eggenberger distributionhttps://projecteuclid.org/euclid.tbilisi/1546570887<strong>M. Mursaleen</strong>, <strong>A. A. H. Al-Abied</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 4, 79--91.</p><p><strong>Abstract:</strong><br/>
In this paper, we give some approximation properties by Stancu-Kantorovich operators based on inverse Pólya-Eggenberger distribution in the polynomial weighted space introduced in the literature and obtain convergence properties of these operators by using Korovkin's theorem. We discuss the direct result and Voronovskaja type asymptotic formula.
</p>projecteuclid.org/euclid.tbilisi/1546570887_20190103220131Thu, 03 Jan 2019 22:01 EST$I$-Convergence of triple difference sequence spaces over $n$-normed spacehttps://projecteuclid.org/euclid.tbilisi/1546570888<strong>Tanweer Jalal</strong>, <strong>Ishfaq Ahmad Malik</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 4, 93--102.</p><p><strong>Abstract:</strong><br/>
The main objective of this paper is to study triple difference sequence spaces over $n$-normed space via the sequence of modulus functions. Some algebraic and topological properties of the newly constructed spaces are also established.
</p>projecteuclid.org/euclid.tbilisi/1546570888_20190103220131Thu, 03 Jan 2019 22:01 ESTOperator approach for orthogonality in linear spaceshttps://projecteuclid.org/euclid.tbilisi/1546570889<strong>Mahdi Iranmanesh</strong>, <strong>Maryam Saeedi Khojasteh</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 4, 103--112.</p><p><strong>Abstract:</strong><br/>
In this paper, we introduce the operator approach for orthogonality in linear spaces. In particular, we represent the concept of orthogonal vectors using an operator associated with them, in normed linear spaces.
</p>projecteuclid.org/euclid.tbilisi/1546570889_20190103220131Thu, 03 Jan 2019 22:01 ESTPerturbed fourth-order Kirchho-type problemshttps://projecteuclid.org/euclid.tbilisi/1546570890<strong>Shapour Heidarkhani</strong>, <strong>Shahin Moradi</strong>, <strong>Giuseppe Caristi</strong>, <strong>Bin Ge</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 4, 113--143.</p><p><strong>Abstract:</strong><br/>
We establish the existence of at least three distinct weak solutions for a perturbed nonlocal fourth-order Kirchhoff-type problem with Navier boundary conditions under appropriate hypotheses on nonlinear terms. Our main tools are based on variational methods and some critical points theorems. We give some examples to illustrate the obtained results.
</p>projecteuclid.org/euclid.tbilisi/1546570890_20190103220131Thu, 03 Jan 2019 22:01 ESTStructural properties for $(m,n)$-quasi-hyperideals in ordered semihypergroupshttps://projecteuclid.org/euclid.tbilisi/1546570891<strong>Ahsan Mahboob</strong>, <strong>Noor Mohammad Khan</strong>, <strong>Bijan Davvaz</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 4, 145--163.</p><p><strong>Abstract:</strong><br/>
In this paper, we first introduce the notion of an $(m,n)$-quasi-hyperideal in an ordered semihypergroup and, then, study some properties of $(m,n)$-quasi-hyperideals for any positive integers $m$ and $n$. Thereafter, we characterize the minimality of an $(m,n)$-quasi-hyperideal in terms of $(m,0)$-hyperideals and $(0,n)$-hyperideals respectively. The relation $\mathcal{Q}_m^n$ on an ordered semihypergroup is, then, introduced for any positive integers $m$ and $n$ and proved that the relation $\mathcal{Q}_m^n$ is contained in the relation $\mathcal{Q}=\mathcal{Q}_1^1$. We also show that, in an $(m,n)$-regular ordered semihypergroup, the relation $\mathcal{Q}_m^n$ coincides with the relation $\mathcal{Q}$. Finally, the notion of an $(m,n)$-quasi-hypersimple ordered semihypergroup is introduced and some properties of $(m,n)$-quasi-hypersimple ordered semihypergroups are studied. We further show that, on any $(m,n)$-quasi-hypersimple ordered semihypergroup, the relations $\mathcal{Q}_m^n$ and $\mathcal{Q}$ are equal and are universal relations.
</p>projecteuclid.org/euclid.tbilisi/1546570891_20190103220131Thu, 03 Jan 2019 22:01 ESTOn the second radical elements of lattice moduleshttps://projecteuclid.org/euclid.tbilisi/1546570892<strong>Narayan Phadatare</strong>, <strong>Vilas Kharat</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 11, Number 4, 165--173.</p><p><strong>Abstract:</strong><br/>
Let $L$ be a $C$-lattice and $M$ be a lattice module over $L$. For a non-zero element $N\in M$, join of all second elements $X$ of $M$ with $X\leq N$ is called the second radical of $N$, and it is denoted by $\sqrt[s]{N}$. In this paper, we study some properties of second radical of elements of $M$ and obtain some related results.
</p>projecteuclid.org/euclid.tbilisi/1546570892_20190103220131Thu, 03 Jan 2019 22:01 ESTOn certain new means generated by generalized trigonometric functionshttps://projecteuclid.org/euclid.tbilisi/1553565622<strong>József Sándor</strong>, <strong>Barkat Ali Bhayo</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 1, 1--16.</p><p><strong>Abstract:</strong><br/>
In this paper, authors generalize logarithmic mean $L$, Neuman-Sándor $M$, two Seiffert means $P$ and $T$ as an application of generalized trigonometric and hyperbolic functions. Moreover, several two-sided inequalities involving these generalized means are established.
</p>projecteuclid.org/euclid.tbilisi/1553565622_20190325220028Mon, 25 Mar 2019 22:00 EDTChebyshev wavelet method for solving radiative transfer equation in a slab mediumhttps://projecteuclid.org/euclid.tbilisi/1553565623<strong>S. Shekarpaz</strong>, <strong>K. Parand</strong>, <strong>H. Azari</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 1, 17--31.</p><p><strong>Abstract:</strong><br/>
In this paper, a numerical method for solving the radiative transfer equation in a slab medium with isotropic scattering is presented. By employing the properties of Chebyshev wavelets together with the collocation method, the problem is reduced into a system of algebraic equations and the approximate solutions are computed. Moreover, numerical examples are included to demonstrate the validity and applicability of this method and a comparison is made with the existing results.
</p>projecteuclid.org/euclid.tbilisi/1553565623_20190325220028Mon, 25 Mar 2019 22:00 EDTSpecial functions, integral transforms with applicationshttps://projecteuclid.org/euclid.tbilisi/1553565624<strong>Arman Aghili</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 1, 33--44.</p><p><strong>Abstract:</strong><br/>
In this study, the author used integral transforms and a method of the exponential nature to deal with the families of fractional differential equations, Stieltjes type singular integral equations and boundary value problems. Certain integrals involving special functions are evaluated. Constructive examples are also provided throughout the paper. The main purpose of this article is to present mathematical results that are useful to researchers in a variety of fields.
</p>projecteuclid.org/euclid.tbilisi/1553565624_20190325220028Mon, 25 Mar 2019 22:00 EDTAspects of invariant submanifolds of a $f_\lambda$-Hsu manifold with complemented frameshttps://projecteuclid.org/euclid.tbilisi/1553565625<strong>Praveen Kumar Mathur</strong>, <strong>Pravin Kumar Srivastava</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 1, 45--54.</p><p><strong>Abstract:</strong><br/>
In this paper, we have discussed the aspects of invariant sub manifolds of a $f_\lambda$-Hsu manifold with complemented frames. The relation between the integrability of Hsu-structure $F$ and that of manifold having $f_\lambda$-Hsu structure with complemented frames has been established. Some other results concerning the normality of $f_\lambda$-Hsu structure with complemented frames have also been obtained.
</p>projecteuclid.org/euclid.tbilisi/1553565625_20190325220028Mon, 25 Mar 2019 22:00 EDTOn projective QTAG-moduleshttps://projecteuclid.org/euclid.tbilisi/1553565626<strong>Fahad Sikander</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 1, 55--68.</p><p><strong>Abstract:</strong><br/>
In this paper we introduce the new class of QTAG-modules namely $\omega_1$-$(\omega+n)$-projective modules, which is an amalgamation of three important classes of modules: $n$-bounded modules, the direct sum of uniserial modules and the countably generated modules. This class is given many equivalent characterizations including being the smallest class containing the $(\omega+n)$-projective modules that is closed with respect to $\omega_1$-bijective homomorphisms.
</p>projecteuclid.org/euclid.tbilisi/1553565626_20190325220028Mon, 25 Mar 2019 22:00 EDTMeasure of noncompactness and semilinear differential equations in Fréchet spaceshttps://projecteuclid.org/euclid.tbilisi/1553565627<strong>Amaria Arara</strong>, <strong>Mouffak Benchohra</strong>, <strong>Fatima Mesri</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 1, 69--81.</p><p><strong>Abstract:</strong><br/>
This paper deals with the existence of mild and integral solutions for a class of functional differential equations. The technique used is a generalization of the classical Darbo fixed point theorem for Fréchet spaces associated with the concept of measure of noncompactness.
</p>projecteuclid.org/euclid.tbilisi/1553565627_20190325220028Mon, 25 Mar 2019 22:00 EDTOn the theory of $4$-th root Finsler metricshttps://projecteuclid.org/euclid.tbilisi/1553565628<strong>Akbar Tayebi</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 1, 83--92.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider exponential change of Finsler metrics. First, we find a condition under which the exponential change of a Finsler metric is projectively related to it. Then we restrict our attention to the $4$-th root metric. Let $F=\sqrt[4]{A}$ be an $4$-th root Finsler metric on an open subset $U\subset \mathbb{R}^n$ and ${\bar F}=e^{\beta/F}F$ be the exponential change of $F$. We show that ${\bar F}$ is locally projectively flat if and only if it is locally Minkowskian. Finally, we obtain necessary and sufficient condition under which ${\bar F}$ be locally dually flat.
</p>projecteuclid.org/euclid.tbilisi/1553565628_20190325220028Mon, 25 Mar 2019 22:00 EDTProperties and applications of the Gould-Hopper-Frobenius-Euler polynomialshttps://projecteuclid.org/euclid.tbilisi/1553565629<strong>Shahid Ahmad Wani</strong>, <strong>Subuhi Khan</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 1, 93--104.</p><p><strong>Abstract:</strong><br/>
This article deals with the introduction of Gould-Hopper based Frobenius-Euler polynomials and derivation of their properties. The summation formulae and operational rule for these polynomials are derived. Also, certain identities for these polynomials are established by using operational formalism.
</p>projecteuclid.org/euclid.tbilisi/1553565629_20190325220028Mon, 25 Mar 2019 22:00 EDTSimulation functions and Boyd-Wong type resultshttps://projecteuclid.org/euclid.tbilisi/1553565630<strong>Suzana Aleksić</strong>, <strong>Sumit Chandok</strong>, <strong>Stojan Radenović</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 1, 105--115.</p><p><strong>Abstract:</strong><br/>
In this paper we give new and much shorter proofs of Boyd-Wong and Meir-Keeler type results. Also, we define a new form of Boyd-Wong type contraction mappings using simulation functions and obtain some sufficient conditions for the existence and uniqueness of a fixed point for such class of mappings in the setting of metric spaces. Also, we present some results regarding the property $P$ for these well-known types of self-mappings.
</p>projecteuclid.org/euclid.tbilisi/1553565630_20190325220029Mon, 25 Mar 2019 22:00 EDTSome new inequalities involving the Katugampola fractional integrals for strongly $\eta$-convex functionshttps://projecteuclid.org/euclid.tbilisi/1553565631<strong>Seth Kermausuor</strong>, <strong>Eze R. Nwaeze</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 1, 117--130.</p><p><strong>Abstract:</strong><br/>
We introduced several new integral inequalities of the Hermite-Hadamard type for strongly $\eta$-convex functions via the Katugampola fractional integrals. Some results in the literature are particular cases of our results.
</p>projecteuclid.org/euclid.tbilisi/1553565631_20190325220029Mon, 25 Mar 2019 22:00 EDTAn alternative proof of the generalized Littlewood Tauberian theorem for Cesàro summable double sequenceshttps://projecteuclid.org/euclid.tbilisi/1553565632<strong>Gökşen Findik</strong>, <strong>İbrahim Çanak</strong>, <strong>Ümit Totur</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 1, 131--148.</p><p><strong>Abstract:</strong><br/>
In this paper, we first examine the relationships between a double sequence and its arithmetic means in different senses (i. e. $(C,1,0)$, $(C,0,1)$ and $(C,1,1)$ means) in terms of slow oscillation in certain senses and investigate some properties of oscillatory behaviors of the difference sequence between the double sequence and its arithmetic means in different senses. Next, we give an alternative proof of the generalized Littlewood Tauberian theorem for Cesàro summability method as an application of the results obtained in the first part.
</p>projecteuclid.org/euclid.tbilisi/1553565632_20190325220029Mon, 25 Mar 2019 22:00 EDTFekete-Szegö results for a class of non-Bazilevič functions defined by convolutionhttps://projecteuclid.org/euclid.tbilisi/1553565633<strong>A. O. Mostafa</strong>, <strong>G. M. El-Hawsh</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 1, 149--158.</p><p><strong>Abstract:</strong><br/>
In the present paper using the principal of subordination we obtain sharp bounds for a class of non-Bazilevič functions with complex order defined by convolution.
</p>projecteuclid.org/euclid.tbilisi/1553565633_20190325220029Mon, 25 Mar 2019 22:00 EDTNew inequalities for $n$-time differentiable functionshttps://projecteuclid.org/euclid.tbilisi/1561082563<strong>Çetin Yildiz</strong>, <strong>M. Emin Özdemir</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 1--15.</p><p><strong>Abstract:</strong><br/>
In this paper, we obtain several inequalities of Ostrowski type that the absolute values of n-time differentiable functions are convex. Also, some applications to special means of real numbers are provided.
</p>projecteuclid.org/euclid.tbilisi/1561082563_20190620220255Thu, 20 Jun 2019 22:02 EDTWeighted sharing and uniqueness for the shifts of meromorphic functionshttps://projecteuclid.org/euclid.tbilisi/1561082564<strong>Chao Meng</strong>, <strong>Gang Liu</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 17--27.</p><p><strong>Abstract:</strong><br/>
In this paper, we deal with the uniqueness problem for $q$-shifts of meromorphic functions. The results obtained in this paper are the $q$-shift analogues of theorems given by Yang and Zhang [Non-existence of meromorphic solution of a Fermat type functional equation, Aequationes Math. 76(2008), 140-150], Chen, Chen and Li [Uniqueness of difference operators of meromorphic functions, J. Ineq. Appl. 2012(2012), Art 48].
</p>projecteuclid.org/euclid.tbilisi/1561082564_20190620220255Thu, 20 Jun 2019 22:02 EDTOn some compact embeddings of a weighted spacehttps://projecteuclid.org/euclid.tbilisi/1561082565<strong>Cihan Unal</strong>, <strong>Ismail Aydin</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 29--45.</p><p><strong>Abstract:</strong><br/>
In this paper, we define an intersection spaces between weighted classical Lebesgue spaces and an amalgam space with two weight functions on a locally compact abelian group with Haar measure. We consider the basic properties of the space such as Banach algebra, translation invariant, Banach module, a generalized type of Segal algebra etc. Also, we investigate some inclusions, compact embeddings in sense to weights and further discuss multipliers of this space.
</p>projecteuclid.org/euclid.tbilisi/1561082565_20190620220255Thu, 20 Jun 2019 22:02 EDTOn pointwise approximation properties of certain nonlinear Bernstein operatorshttps://projecteuclid.org/euclid.tbilisi/1561082566<strong>H. Erhan Altin</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 47--58.</p><p><strong>Abstract:</strong><br/>
The present study is concerned with the nonlinear Bernstein type operators $NB_{n}f$, acting on bounded functions, where the kernel function of the operators provide some convenient assumptions. Especially, some pointwise convergence results for these type operators are achieved at a generalized Lebesgue point of the function $f$.
</p>projecteuclid.org/euclid.tbilisi/1561082566_20190620220255Thu, 20 Jun 2019 22:02 EDTA new method for the solution of Volterra-Fredholm integro-differential equationshttps://projecteuclid.org/euclid.tbilisi/1561082567<strong>Yousef Jafarzadeh</strong>, <strong>Reza Ezzati</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 59--66.</p><p><strong>Abstract:</strong><br/>
In the present study, we investigate the hybrid of Taylor series and Block pulse functions solutions of higher order linear integro-differential Volterra-Fredholm equations (IDVFE) by using a new method. This method transforms IDVFE into the matrix equations which correspond to a system of linear algebraic equations. Some numerical results are also given to illustrate the efficiency of the method.
</p>projecteuclid.org/euclid.tbilisi/1561082567_20190620220255Thu, 20 Jun 2019 22:02 EDTParallelism in Hilbert $K(\mathcal{H})$-moduleshttps://projecteuclid.org/euclid.tbilisi/1561082568<strong>M. Mohammadi Gohari</strong>, <strong>M. Amyari</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 67--75.</p><p><strong>Abstract:</strong><br/>
Let $\mathcal{H}$ be a Hilbert space and $K(\mathcal{H})$ be the $C^*$-algebra of compact operators on $\mathcal{H}$. In this paper, we present some characterizations of the norm-parallelism for elements of a Hilbert $K(\mathcal{H})$-module $\mathcal{E}$ by employing the minimal projections on $\mathcal{H}$. In addition, we give some equivalence assertions about the norm-parallelism of compact operators on a Hilbert $C^*$-module.
</p>projecteuclid.org/euclid.tbilisi/1561082568_20190620220255Thu, 20 Jun 2019 22:02 EDTMeromorphic solutions of nonlinear ordinary differential equationshttps://projecteuclid.org/euclid.tbilisi/1561082569<strong>P. G. Siddheshwar</strong>, <strong>A. Tanuja</strong>, <strong>Subhas S. Bhoosnurmath</strong>, <strong>Mahesh Barki</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 77--88.</p><p><strong>Abstract:</strong><br/>
Meromorphic solutions of a class of nonlinear ordinary differential equations in $g(z)$ under the assumption that finite-degree polynomials with coefficients as small functions of $g$ share one-value with the nonlinear differential operator of the equation. The concept of sharing one-value is used in the sense of counting multiplicity or ignoring multiplicity.
</p>projecteuclid.org/euclid.tbilisi/1561082569_20190620220255Thu, 20 Jun 2019 22:02 EDTAlmost automorphic solutions for neutral type CNNs with time-varying delays and $D$ operator on time scaleshttps://projecteuclid.org/euclid.tbilisi/1561082570<strong>Bing Li</strong>, <strong>Yongkun Li</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 89--100.</p><p><strong>Abstract:</strong><br/>
In this paper, we propose a new concept of almost automorphic functions on a new type of almost periodic time scales. Based on inequality analysis techniques on time scales, the exponential dichotomy of linear dynamic equations on time scales and the Banach's fixed point theorem, we establish the existence and global exponential stability of almost automorphic solutions for a class of neutral type cellular neural networks with time-varying delays and $D$ operator on time scales. We give a numerical example to illustrate the feasibility of our results.
</p>projecteuclid.org/euclid.tbilisi/1561082570_20190620220255Thu, 20 Jun 2019 22:02 EDTProduct of Sheffer sequences: properties and exampleshttps://projecteuclid.org/euclid.tbilisi/1561082571<strong>Mumtaz Riyasat</strong>, <strong>Subuhi Khan</strong>, <strong>Shakir Shah</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 101--118.</p><p><strong>Abstract:</strong><br/>
This article is written with an objective to explore the product of two Sheffer sequences. This article is an attempt to explore such type of product which extends the possibility to consider hybrid type Sheffer polynomials. It is important to remark that although this product can be viewed as the umbral composition of two Sheffer sequences but the results related to this product cannot be deduced from the results of the Sheffer sequences. The set of this product of Sheffer sequences is also a non-abelian group and thus convoluting different members of Sheffer class allows us to consider a number of hybrid type special polynomials as its members. Certain results for this class including the quasi-monomiality and determinant form are established. The article concludes with the possibility of considering the product of $n$-Sheffer sequences.
</p>projecteuclid.org/euclid.tbilisi/1561082571_20190620220255Thu, 20 Jun 2019 22:02 EDTDegree of approximation of genuine Lupaş-Durrmeyer operatorshttps://projecteuclid.org/euclid.tbilisi/1561082572<strong>Nesibe Manav</strong>, <strong>Nurhayat Ispir</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 119--135.</p><p><strong>Abstract:</strong><br/>
The present paper deals with the rate of convergence of genuine type Durrmeyer operators having Lupaş-Szász type basis functions. We study some direct estimates to give the degree of approximation to continuous functions. Further, we investigate pointwise convergence for functions with derivative of bounded variations.
</p>projecteuclid.org/euclid.tbilisi/1561082572_20190620220255Thu, 20 Jun 2019 22:02 EDTSome Qi-type integral inequalities involving several weight functionshttps://projecteuclid.org/euclid.tbilisi/1561082573<strong>Jan-David Hardtke</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 137--152.</p><p><strong>Abstract:</strong><br/>
We prove some integral inequalities related to Feng Qi's inequality from [ Several integral inequalities , J. Inequal. Pure Appl. Math. 1 (2000), No. 2, 7p., Article No. 19] and obtain a few corollaries.
</p>projecteuclid.org/euclid.tbilisi/1561082573_20190620220255Thu, 20 Jun 2019 22:02 EDTHigher chromatic analogues of twisted $K$-theoryhttps://projecteuclid.org/euclid.tbilisi/1561082574<strong>Mehdi Khorami</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 153--162.</p><p><strong>Abstract:</strong><br/>
In this paper we introduce a new family of twisted $K(n)$-local homology theories. These theories are given by the spectra $R_n= E_n^{hS\mathbb G_n}$, twisted by a class $H\in H^{n+2}(X, \mathbb Z_p)$. Here $E_n^{hS\mathbb G_n}$ are the homotopy fixed point spectra under the action of the subgroup $S\mathbb G_n$ of the Morava stabilizer group where $S\mathbb G_n$ is the kernel of the determinant homomorphism $\text{det}:\mathbb G_n\to \mathbb Z_p^\times$. These spectra were utilized in [8] by C. Westerland to study higher chromatic analogues of the J-homomorphism. We investigate some of the properties of these new twisted theories and discuss why we consider them as a generalization of twisted $K$-theory to higher chromatic levels.
</p>projecteuclid.org/euclid.tbilisi/1561082574_20190620220255Thu, 20 Jun 2019 22:02 EDTCoefficient estimates for a general subclass of $m$-fold symmetric bi-univalent functionshttps://projecteuclid.org/euclid.tbilisi/1561082575<strong>Ahmad Motamednezhad</strong>, <strong>Safa Salehian</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 163--176.</p><p><strong>Abstract:</strong><br/>
In the present paper, we introduce and investigate an interesting subclass ${\mathcal B}_{{\Sigma}_m}^{h,p}(\lambda,\gamma)$ of $m$-fold symmetric bi-univalent functions in the open unit disk $\mathbb{U}$. Furthermore, we obtain estimates on the coefficients $|a_{m+1}|$ and $|a_{2m+1}|$ for functions belonging to this subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.
</p>projecteuclid.org/euclid.tbilisi/1561082575_20190620220255Thu, 20 Jun 2019 22:02 EDTInequalities for complex rational functionshttps://projecteuclid.org/euclid.tbilisi/1561082576<strong>T. Shahmansouri</strong>, <strong>M. Bidkham</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 2, 177--185.</p><p><strong>Abstract:</strong><br/>
In this paper, we consider a class of rational functions $r(s(z))$ of degree at most $mn$, where $s(z)$ is a polynomial of degree $m$ and obtain a certain sharp compact generalization of well-known inequalities for rational functions.
</p>projecteuclid.org/euclid.tbilisi/1561082576_20190620220255Thu, 20 Jun 2019 22:02 EDTSome new $k$-fractional trapezium-like integral inequalities via generalized relative semi-$(r;m,h_{1},h_{2})$-preinvex mappings and applicationshttps://projecteuclid.org/euclid.tbilisi/1569463229<strong>Artion Kashuri</strong>, <strong>Muhammad Adil Khan</strong>, <strong>Rozana Liko</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 1--19.</p><p><strong>Abstract:</strong><br/>
In this article, we first presented a new general identity concerning differentiable mappings defined on $m$-invex set via $k$-fractional integrals. By using the concept of generalized relative semi-$(r;m,h_{1},h_{2})$-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to trapezium-like integral inequalities via $k$-fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article. Applications to special means for trapezium-like integral inequalities via $k$-fractional integrals are provided as well.
</p>projecteuclid.org/euclid.tbilisi/1569463229_20190925220040Wed, 25 Sep 2019 22:00 EDTA discrete orthogonal polynomials approach for coupled systems of nonlinear fractional order integro-differential equationshttps://projecteuclid.org/euclid.tbilisi/1569463232<strong>L. Moradi</strong>, <strong>F. Mohammadi</strong>, <strong>D. Conte</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 21--38.</p><p><strong>Abstract:</strong><br/>
This paper develops a numerical approach for solving coupled systems of nonlinear fractional order integro-differential equations(NFIDE). Shifted discrete Chebyshev polynomials (SDCPs) have been introduced and their attributes have been checked. Fractional operational matrices for the orthogonal polynomials are also acquired. A numerical algorithm supported by the discrete orthogonal polynomials and operational matrices are used to approximate solution of coupled systems of NFIDE. The operational matrices of fractional integration and product are applied for approximate the unknown functions directly. These approximations were put in the coupled systems of NFIDE. A comparison has been made between the absolute error of approximate solutions of SDCPs method with previous published. The gained numerical conclusions disclose that utilizing discrete Chebyshev polynomials are more efficient in comparison to the other methods.
</p>projecteuclid.org/euclid.tbilisi/1569463232_20190925220040Wed, 25 Sep 2019 22:00 EDT$(\epsilon-\delta)$ conditions and fixed point theoremshttps://projecteuclid.org/euclid.tbilisi/1569463233<strong>Ravindra K. Bisht</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 39--49.</p><p><strong>Abstract:</strong><br/>
In this paper, we prove some fixed point theorems under generalized $(\epsilon-\delta)$ type rational contractions in which the fixed point may be a point of discontinuity. Our results generalize and improve a host of well-known fixed point theorems existing in the literature. In addition to it we give a fixed point theorem for $(\epsilon-\delta)$ non-expansive mappings in metric spaces. Several examples are given to illustrate our results.
</p>projecteuclid.org/euclid.tbilisi/1569463233_20190925220040Wed, 25 Sep 2019 22:00 EDTOperator splitting method for numerical solution of modified equal width equationhttps://projecteuclid.org/euclid.tbilisi/1569463234<strong>İhsan Çelikkaya</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 51--67.</p><p><strong>Abstract:</strong><br/>
In this manuscript, numerical solutions of the equations in the form of $u_{t}=Au+B(u)$ have been sought for, where $A$ and $B$ are linear and nonlinear operators, respectively. The modified equal width (MEW) equation has been converted into two sub problems. Then, the sub problems were solved according to the Strang splitting scheme by applying the cubic B-spline collocation finite element method. Thus, more accurate results of the equation MEW have been obtained than those non-splitting users. In order to test the accuracy and efficiency of the present method; single soliton, interaction of two solitons and Maxwellian initial condition pulse problems have been considered. Moreover, the stability analysis of each sub problem has been investigated by von-Neumann analysis method.
</p>projecteuclid.org/euclid.tbilisi/1569463234_20190925220040Wed, 25 Sep 2019 22:00 EDTTopological Quillen localization of structured ring spectrahttps://projecteuclid.org/euclid.tbilisi/1569463235<strong>John E. Harper</strong>, <strong>Yu Zhang</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 69--91.</p><p><strong>Abstract:</strong><br/>
The aim of this short paper is two-fold: (i) to construct a $\mathsf{TQ}$-localization functor on algebras over a spectral operad $\mathcal{O}$, in the case where no connectivity assumptions are made on the $\mathcal{O}$-algebras, and (ii) more generally, to establish the associated $\mathsf{TQ}$-local homotopy theory as a left Bousfield localization of the usual model structure on $\mathcal{O}$-algebras, which itself is almost never left proper, in general. In the resulting $\mathsf{TQ}$-local homotopy theory, the ''weak equivalences'' are the $\mathsf{TQ}$-homology equivalences, where ''$\mathsf{TQ}$-homology'' is short for topological Quillen homology, which is also weakly equivalent to stabilization of $\mathcal{O}$-algebras. More generally, we establish these results for $\mathsf{TQ}$-homology with coefficients in a spectral algebra $\mathcal{A} $. A key observation, that goes back to the work of Goerss-Hopkins on moduli problems, is that the usual left properness assumption may be replaced with a strong c ofibration condition in the desired subcell lifting arguments: Our main result is that the $\mathsf{TQ}$-local homotopy theory can be established (e.g., a semi-model structure in the sense of Goerss-Hopkins and Spitzweck, that is both cofibrantly generated and simplicial) by localizing with respect to a set of strong cofibrations that are $\mathsf{TQ}$-equivalences.
</p>projecteuclid.org/euclid.tbilisi/1569463235_20190925220040Wed, 25 Sep 2019 22:00 EDTSolutions to some systems of adjointable operator equations over Hilbert $C^*$-moduleshttps://projecteuclid.org/euclid.tbilisi/1569463236<strong>Zahra Niazi Moghani</strong>, <strong>Mahnaz Khanehgir</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 93--107.</p><p><strong>Abstract:</strong><br/>
In this paper, by using operator matrix techniques, we present necessary and sufficient conditions for the existence of a solution to the system of equations $AXD+FX^{*}B=C,$ $GXF^{*}+FX^{*}G^{*}=H$ for adjointable operators between Hilbert $C^*$-modules, and derive an expression for the general solution to the system. We establish necessary and sufficient conditions for the existence of a solution to the system of adjointable operator equations $AXF=H_{1},$ $CXD=H_{2},$ $BXD=H_{3}$ over Hilbert $C^*$-modules. Some of the findings of this paper extend some known results in the literature.
</p>projecteuclid.org/euclid.tbilisi/1569463236_20190925220040Wed, 25 Sep 2019 22:00 EDTExact solutions of nonlinear evolution equations using the extended modified Exp(-$\Omega (\xi )$) function methodhttps://projecteuclid.org/euclid.tbilisi/1569463237<strong>Berat Karaagac</strong>, <strong>Selcuk Kutluay</strong>, <strong>Nuri Murat Yagmurlu</strong>, <strong>Alaattin Esen</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 109--119.</p><p><strong>Abstract:</strong><br/>
Obtaining exact solutions of the evolution equation is one of the very important subjects in mathematics, science and technology. For this purpose, many different methods have been constructed and developed. In this article, a new technique which is called extended modified Exp(-$\Omega (\xi )$) function method is going to be studied for seeking new exact solutions of Burger-Fisher equation and Phi Four equation. The method is capable of deriving many number of solutions. With the aid of the method, various exact solutions including trigonometric, hyperbolic and rational solutions have been obtained and using a software the graphical representation of the solutions have been presented. In conclusion, we can say that the present method can also be used for the solutions of a wide range of problems.
</p>projecteuclid.org/euclid.tbilisi/1569463237_20190925220040Wed, 25 Sep 2019 22:00 EDTOn moduli of smoothness of functions in Orlicz spaceshttps://projecteuclid.org/euclid.tbilisi/1569463238<strong>Sadulla Z. Jafarov</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 121--129.</p><p><strong>Abstract:</strong><br/>
In this work the estimate about modulus of smoothness of the derivatives of the functions is obtained in Orlicz spaces. The relations between the modulus of smoothness of the functions with $n$th partial and Vallée-Poussin sums of the Fourier series in Orlicz spaces are studied.
</p>projecteuclid.org/euclid.tbilisi/1569463238_20190925220040Wed, 25 Sep 2019 22:00 EDTConnection and duplication formulas for the Boas-Buck-Appell polynomialshttps://projecteuclid.org/euclid.tbilisi/1569463239<strong>Tabinda Nahid</strong>, <strong>Subuhi Khan</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 131--139.</p><p><strong>Abstract:</strong><br/>
The present paper conduct to introduce the connection and duplication formulas associated with the Boas-Buck-Appell polynomials. Examples providing the analogues results for certain members related to the Boas-Buck-Appell polynomials are considered.
</p>projecteuclid.org/euclid.tbilisi/1569463239_20190925220040Wed, 25 Sep 2019 22:00 EDTFinding hybrid relatives of the Bessel polynomialshttps://projecteuclid.org/euclid.tbilisi/1569463240<strong>Mahvish Ali</strong>, <strong>Subuhi Khan</strong>, <strong>Shakeel Ahmad Naikoo</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 141--158.</p><p><strong>Abstract:</strong><br/>
In this work, the 2D-Appell and the Bessel polynomials are combined to introduce the family of the 2D-Appell-Bessel polynomials. The generating function, quasi-monomial properties, series definition and determinant form of these polynomials are established. Examples of some members belonging to this family are considered. The graphs of some hybrid special polynomials are also drawn for suitable values of the indices.
</p>projecteuclid.org/euclid.tbilisi/1569463240_20190925220040Wed, 25 Sep 2019 22:00 EDTA Lumped Galerkin finite element method for the generalized Hirota-Satsuma coupled KdV and coupled MKdV equationshttps://projecteuclid.org/euclid.tbilisi/1569463241<strong>Nuri Murat Yagmurlu</strong>, <strong>Berat Karaagac</strong>, <strong>Alaattin Esen</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 159--173.</p><p><strong>Abstract:</strong><br/>
In the present study, a Lumped Galerkin finite element method using quadratic B-splines has been applied to the generalized Hirota-Satsuma coupled Korteweg de Vries (KdV) and coupled modified Korteweg-de Vries (mKdV) equations. The numerical solutions of discretized equations using Lumped Galerkin finite element method have been obtained using the fourth order Runge-Kutta method which is widely used for the solution of ordinary differential equation system. The numerical solutions obtained for various space and time values have been compared with exact ones using the error norms $L_{2}$ and $L_{\infty}$. Lumped Galerkin finite element method is an effective one which can be applied to a wide range of nonlinear evolution equations.
</p>projecteuclid.org/euclid.tbilisi/1569463241_20190925220040Wed, 25 Sep 2019 22:00 EDTStability and non-stability of generalized radical cubic functional equation in quasi-$\beta$-Banach spaceshttps://projecteuclid.org/euclid.tbilisi/1569463242<strong>Iz-iddine EL-Fassi</strong>, <strong>John Michael Rassias</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 175--190.</p><p><strong>Abstract:</strong><br/>
The object of this paper is to solve the generalized radical cubic functional equation, and discuss the stability problem in quasi-$\beta$-Banach spaces and then the stability by using subadditive and subquadratic functions in ($\beta, p$)-Banach spaces for the generalized radical cubic functional equation. Also certain non-stability results are investigated via specific counterexamples. Our results are generalization of the main results which are established by Z. Alizadeh and A. G. Ghazanfari in 2016.
</p>projecteuclid.org/euclid.tbilisi/1569463242_20190925220040Wed, 25 Sep 2019 22:00 EDTOn $(4, 5)$-regular bipartitions with odd parts distincthttps://projecteuclid.org/euclid.tbilisi/1569463243<strong>M. S. Mahadeva Naika</strong>, <strong>T. Harishkumar</strong>. <p><strong>Source: </strong>Tbilisi Mathematical Journal, Volume 12, Number 3, 191--208.</p><p><strong>Abstract:</strong><br/>
In his work, K. Alladi considered the partition function $pod(n)$, the number of partitions of an integer $n$ with odd parts distinct (the even parts are unrestricted). He obtained a series expansion for the product generating function of these partitions. Later Hirschhorn and Sellers obtained some internal congruences involving the infinite families and Ramanujan's type congruences for $pod(n)$. Let $B_{4, 5}(n)$ denote the number of $(4, 5)$-regular bipartitions of a positive integer $n$ with odd parts distinct. In this paper, we establish many infinite families of congruences modulo powers of $2$ for $B_{4, 5}(n)$.
</p>projecteuclid.org/euclid.tbilisi/1569463243_20190925220040Wed, 25 Sep 2019 22:00 EDT