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.

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].

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.

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 $f$.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.