Let $\mathcal{SB}(X,Y)$ be the set of the bounded sublinear operators from a Banach space $X$ into a complete Banach lattice $Y$. In the present paper, we introduce to this category the concept of strongly $p-$summing sublinear operators. We give an analogue to Pietsch's domination theorem and study some comparisons between linear and sublinear operators.

In this paper, we investigate a second-order Sturm-Liouville boundary value problem depending on the parameter $\lambda$. For any $\lambda$ in some explicitly determined open interval, the boundary value problem admits multiple generalized solutions by using very recent three critical points theorems stated in a paper by G. Bonanno (J. Math. Anal. Appl. 29 (2004), 600-614).

In this paper, we first give a relation between the adjacency spectral radius and the $Q$-spectral radius of a graph. Then using this result, we further give some new sharp upper bounds on the adjacency spectral radius of a graph in terms of degrees and the average 2-degrees of vertices. Some known results are also obtained.

A differential equation characterizing the dual Lorentzian spherical curves and an explicit solution of this differential equation are given. Also, without the precondition on the dual torsion is nowhere pure-dual, a necessary and sufficient condition for a curve to be dual Lorentzian spherical is presented. In addition, thanks to dual geodesic trihedron, torsion and curvature of dual Lorentzian curve $\overset{\rightarrow}{\hat{x}(s)}$ have been calculated.

In this paper we describe annihilators of principal ideals of exterior algebras. For odd elements we establish formulae for dimensions of their principal ideals and their annihilators. For even elements we exhibit (multiplicative) generators for annihilator ideals.

In this note we study modules with the property that the intersection of two direct summands is essential in a direct summand (SIP-extending). Amongst other results we show that the class of right SIP-extending modules is neither closed under direct sums nor Morita invariant. Further we deal with direct summands of a SIP-extending module and SIP-extending matrix rings.

We study a subclass of Sheffer sequences denominated Appell sequences. Using methods of the so-called umbral calculus in conjunction with general results of nuclear Fréchet spaces and the theory of Köthe sequence spaces, we give necessary and sufficient conditions for an Appell sequence to be a basis.

Let $X$ be a fuzzy path connected space and $H_{a_{\lambda}}$ be the fundamental group of $X$ based for any $a_{\lambda} \in X$, that is $\pi_{1}(X,a_{\lambda})$. Constructing the fuzzy sheaf of the fundamental groups of $X$, it is shown that there is a covariant functor from the category of fuzzy path connected topological spaces and fuzzy continuous mappings to the category of fuzzy sheaves and fuzzy sheaf homomorphisms.

In this paper we prove the following result. Let $A$ be a semisimple $H^{\ast}-$algebra and let $T: A \rightarrow A$ be an additive mapping satisfying the relation $2T(x^{m+n+1}) = x^{m} T(x) x^{n} + x^{n} T(x) x^{m}$, for all $x \in A$ and some nonnegative integers $m,n$ such that $ m+n \neq 0$. In this case $T$ is a left and a right centralizer.

The nonlocal boundary value problem for hyperbolic-parabolic equations \[ \left\{ \!\! \begin{array}{c} \frac{d^{2}u(t)}{dt^{2}}+Au(t)=f(t)(0\leq t\leq 1),\frac{du(t)}{dt} +Au(t)=g(t)(-1\leq t\leq 0), \\ u(-1)\!=\!\sum\limits_{i=1}^{N}\alpha _{i}u\left( \mu _{i}\right) \!+\!\sum\limits_{i=1}^{L}\beta _{i}u^{\prime }\left( \lambda _{i}\right) \!+\!\varphi ,\sum\limits_{i=1}^{N}|\alpha _{i}|,\sum\limits_{i=1}^{L}\left\vert \beta _{i}\right\vert \leq 1,0\!\lt \!\mu _{i},\lambda _{i}\!\leq\! 1 \end{array} \right. \] for differential equation in a Hilbert space $H$, with the self-adjoint positive definite operator $A$ is considered. The stability estimates for the solution of this problem are established. In applications, the stability estimates for the solutions of the mixed type bundary value problems for hyperbolic-parabolic equations are obtained.

In this paper, we establish a sharp maximal inequality for Morrey spaces with a Radon measure $\mu$ satisfying certain growth condition, which is not necessarily doubling. As an application, we obtain the boundedness of commutators generated by singular integral or fractional integrals with RBMO functions in Morrey spaces.

In this paper, we introduce the uniform forward sets of $C(X)$ and show that each totally bounded set of $C(X)$ is uniform forward set, moreover, we prove that the uniform forward sets of $C(X)$ are just the largest subset family of $C(X)$ on which each $C(X)$-evaluation convergent operator series is uniformly convergent.

Let $X$ and $Y$ be Banach spaces such that $X$ has an unconditional basis. Then $X \hat{\otimes} Y$, the projective tensor product of $X$ and $Y$, contains no copy of $\ell_1$ if and only if both $X$ and $Y$ contain no copy of $\ell_1$ and each continuous linear operator from $X$ to $Y^\ast$ is compact.

Let $\mu$ be a Borel measure on $\mathbb{R}^d$ which may be non doubling. The only condition that $\mu$ must satisfy is $\mu(Q) \leq c_0 l(Q)^n$ for any cube $Q \subset \mathbb{R}^d$ with sides parallel to the coordinate axes and for some fixed $n$ with $0 \lt n \leq d$. This paper is to develop the vector valued commutator theory in the context of the non-thomogeneous spaces. As an application, the boundedness of the maximal commutator of any Calderón-Zygmund operator on the non-homogeneous space with a $RBMO(\mu)$ function introduced by Tolsa in [9] is obtained.

In this paper the authors established some sharp estimates for a class of the parametrized Littlewood-Paley operators. Using the result the authors give the weighted $L^p$ bounds of the parametrized area integral and Littlewood-Paley $g_\lambda^*$ function.

We define a Hardy-Sobolev space and give its atomic decomposition. As an application of the decomposition we prove a div-curl lemma.

Let $\alpha \gt -1$, $U$ be the open unit disk in $\mathbb C$ and denote by $H(U)$ the set of all holomorphic functions on $U$. Let $C_\varphi$ be a composition operator induced by an analytic self-map $\varphi$ of $U$. Composition operators $C_\varphi$ on the weighted Hilbert Bergman space ${\mathcal A}^2_\alpha(U) = \big\{f \in H(U) \;|\; \int_U |f(z)|^2(1-|z|^2)^\alpha dm(z) \lt \infty \big\}$ are considered. We investigate when convergence of sequences $(\varphi_n)$ of symbols to a given symbol $\varphi$, implies the convergence of the induced composition operators. We give a necessary and sufficient condition for a sequence of Hilbert-Schmidt composition operators $(C_{\varphi_n})$ to converge in Hilbert-Schmidt norm to $C_\varphi$, and we obtain a sufficient condition for convergence in operator norm.

Let $R$ be a ring with an identity (not necessary commutative) and let $M$ be a left $R$-module. In this paper we will introduce the concept of a comultiplication $R$-module and we will obtain some related results.

We enlarge two weak majorization relations of the vectors to strong majorization relations of the vectors. An improvement of the discrete Steffensen’s inequalities is established by the related propositions in the theory of majorization.

In [Acta Math. 80(1948),167-190], G. G. Lorentz characterized almost convergent sequences in $\mathbb R$ (or in $\mathbb C$) in terms of the concept of uniform convergence of the de la Vallée-Poussin means. In this paper, we give a further study on such kind of convergence for any Hilbert space or $L^p(T)$, where $1 \le p \le \infty$. Two new Cauchy forms for almost convergence are established. We prove that any of them is equivalent to the one established by Miller and Orhan. We use these forms to characterize almost convergent sequences in the aforementioned spaces in terms of coefficients.

Some oscillation theorems are established by the averaging technique for the second order nonlinear neutral delay differential equation $$ \begin{array}{l} (r(t) |x^{\prime}(t)|^{\gamma-1} x^{\prime}(t))^{\prime} + q_1(t) |y(t-\sigma_1)|^{\alpha-1} y(t-\sigma_1) \\ \hspace{5mm} + q_2(t) |y(t-\sigma_2)|^{\beta-1} y(t-\sigma_2) = 0, \quad t \geq t_0, \end{array} $$ where $x(t) = y(t) + p(t) y(t-\tau)$, $\tau$, $\sigma_1$ and $\sigma_2$ are nonnegative constants, $\alpha$, $\beta$ and $\gamma$ are positive constants, and $r$, $p$, $q_1$, $q_2 \in C([t_0, \infty), \mathbb{R})$. The results obtained here essentially improve some known results in the literature. In particular, two interesting examples that point out the applications of our results are also included.

We obtain a relative volume comparison estimate in the universal covering space under bounds on the integral Ricci curvature and the weak $C^1$-norm of metric. From this volume comparison, we obtain similar results on the fundamental group as in [1,7,8].