We introduce the space Bw(ℓ2) of linear (unbounded) operators on ℓ2 which map decreasing sequences from ℓ2 into sequences from ℓ2 and we find some classes of operators belonging either to Bw(ℓ2) or to the space of all Schur multipliers on Bw(ℓ2). For instance we show that the space B(ℓ2) of all bounded operators on ℓ2 is contained in the space of all Schur multipliers on Bw(ℓ2).

We define Sobolev capacity on the generalized Sobolev space W1, p(⋅)(ℝn). It is a Choquet capacity provided that the variable exponent p:ℝn→[1,∞) is bounded away from 1 and ∞. We discuss the relation between the Hausdorff dimension and the Sobolev capacity. As another application we study quasicontinuous representatives in the space W1, p(⋅)(ℝn).

In this paper, we prove that if is a -separable bounded subset of , then every convex function is Gteaux differentiable at a dense subset of if and only if every subset of is weakly dentable. Moreover, we also prove that if is a closed convex set, then if and only if is a weakly exposed point of exposed by . Finally, we prove that is an Asplund space if and only if, for every...

By using the theory of fixed-point index on cone for differentiable operators, spectral radii of some related linear integral operators, and properties of Green’s function, the existence of multiple positive solutions to a nonlinear fractional differential system with integral boundary value conditions and a parameter is established. At last, some examples are also provided to...

In this paper, we give the sufficient conditions on Orlicz-Cesáro mean sequence spaces , where is an Orlicz function such that the class of all bounded linear operators between arbitrary Banach spaces with its sequence of numbers which belong to forms an operator ideal. The completeness and denseness of its ideal components are specified and constructs a pre-quasi Banach operator...

Let be a Schrödinger operator, where is the Laplacian on and the nonnegative potential belongs to the reverse Hölder class for . The Riesz transform associated with the operator is denoted by and the dual Riesz transform is denoted by . In this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder...

In this study, it is proposed to define bivariate Chlodowsky variant of -Bernstein-Stancu-Schurer operators. Therefore, Korovkin-type approximation theorems and the error of approximation by using full modulus of continuity are presented. Beside this, we introduce a generalization of the bivariate Chlodowsky variant of -Bernstein-Stancu-Schurer operators and investigate its...

In this paper, we characterize the closure of the Morrey space in the Bloch space. Furthermore, the boundedness and compactness of composition operators from the Bloch space to the closure of the Morrey space in the Bloch space are investigated.

We use the Baernstein star-function to investigate several questions about the integral means of the convolution of two analytic functions in the unit disc. The theory of univalent functions plays a basic role in our work.

As is well known, the extreme points and strongly extreme points play important roles in Banach spaces. In this paper, the criterion for strongly extreme points in Orlicz spaces equipped with s-norm is given. We complete solved criterionOrlicz space that generated by Orlicz function. And the sufficient and necessary conditions for middle point locally uniformly convex in Orlicz...

The aim of this paper is to establish existence and uniqueness of a positive continuous solution to the following singular nonlinear problem. , where and denotes a nonnegative continuous function that might have the property of being singular at and /or and which satisfies certain condition associated to Karamata class. We emphasize that the nonlinearity might also be singular at...

In this work, two Geraghty type contractions are introduced in -metric spaces, and some fixed point theorems about the contractions are proved. At the end of this article, a theorem about unique solution of an integral function is proved.

In this paper, we consider the following higher-order semipositone nonlocal Riemann-Liouville fractional differential equation and where and are the standard Riemann-Liouville fractional derivatives. The existence results of positive solution are given by Guo-krasnosel’skii fixed point theorem and Schauder’s fixed point theorem.

In the article, we present several conformable fractional integrals’ versions of the Hermite-Hadamard type inequalities for GG- and GA-convex functions and provide their applications in special bivariate means.

The main purpose of this paper is to investigate the growth of several entire functions represented by double Dirichlet series of finite logarithmic order, -order. Besides, we also study some properties on the maximum modulus of double Dirichlet series and its partial derivative. Our results are extension and improvement of previous results given by Huo and Liang.

This paper analyzes the optimal reinsurance strategy for insurers with a generalized mean-variance premium principle. The surplus process of the insurer is described by the diffusion model which is an approximation of the classical Cramér-Lunderberg model. We assume the dynamic VaR constraints for proportional reinsurance. We obtain the closed form expression of the optimal...

We consider a ratio-dependent predator-prey model under zero Dirichlet boundary condition. By using topological degree theory and fixed index theory, we study the necessary and sufficient conditions for the existence of positive solutions. Then we present the asymptotic behavior analysis of positive solutions, by bifurcation theory and energy estimates.

This paper is devoted to give several improvements of some known facts in lineability approach. In particular, we prove that (i) the set of continuous mappings from the unit interval onto the unit square contains a closed, -semigroupable convex subset, (ii) the set of pointwise convergent martingales with is -lineable, (iii) the set of martingales converging in measure but not...

In this paper, we will consider the stationary Stokes equations with the periodic boundary condition and we will study approximation property of the solutions by using the properties of the Fourier series. Finally, we will discuss that our estimation for approximate solutions is optimal.

In this paper, by using the spectral analysis of the relevant linear operator and Gelfand’s formula, some properties of the first eigenvalue of a fractional differential equation were obtained; combining fixed point index theorem, sufficient conditions for the existence of positive solutions are established. An example is given to demonstrate the application of our main results.

We define Sobolev capacity on the generalized Sobolev space W1, p(⋅)(ℝn). It is a Choquet capacity provided that the variable exponent p:ℝn→[1,∞) is bounded away from 1 and ∞. We discuss the relation between the Hausdorff dimension and the Sobolev capacity. As another application we study quasicontinuous representatives in the space W1, p(⋅)(ℝn).

It is known that the space L1(μ) of complex functions which are integrable with respect to a vector measure μ taking values in a (not neessarily complete) locally convex space is not an ideal, in general. We discuss several natural properties which L1(μ) may or may not possess and consider various implications between these properties. For a particular class of properties...

We study local uniform convexity and Kadec-Klee type properties in K-interpolation spaces of Lorentz couples. We show that a wide class of Banach couples of (commutative and) non-commutative Lorentz spaces possess the (so-alled) (DGL)-property originally introduced by Davis, Ghoussoub and Lindenstrauss in the context of renorming order continuous Banach latties. This property is...

Let s≺0. The author obtains some new frames for Besov spaces Bpqs(ℝn) with 1≤p, q≤∞ and Triebel-Lizorkin spaces Fpqs(ℝn) with 1≺p≺∞ and 1≺q≤∞ by a dual method via the subatomic characterizations of these spaces when s≻0.

A question about comparing norms of difference operators that was raised in [1] and presented at the Fourth ISAAC Congress is answered in the affirmative.