Mappings In Banach Spaces Research Articles

Fixed point approximation for a class of generalized nonexpansive multi-valued mappings in Banach spaces

In this paper, we propose a new iteration process, called multi-valued F-iteration process, for the approximation of fixed points. We introduce a new class of multi-valued generalized nonexpansive mappings satisfying a B_{gamma ,mu } property. Moreover, we establish certain weak and strong convergence theorems in uniformly convex Banach spaces. We also discuss the stability of the modified F-iteration process. Furthermore, a numerical example is presented to illustrate the superiority of our results.

A Fuglede type theorem for Fourier multiplier operators

Let E be a translation invariant Banach function space over an infinite compact abelian group G and Mφ be a Fourier multiplier operator (with symbol φ) acting on E. It is assumed that E has order continuous norm and that E is reflection invariant (which ensures that φ̄ is also a multiplier symbol for E). The following Fuglede type theorem is established. Whenever T is a bounded linear operator on E satisfying MφT=TMφ, then also Mφ̄T=TMφ̄.

Linear operators and their commutators generated by Calderón–Zygmund operators on generalized Morrey spaces associated with ball Banach function spaces

Linear operators and their commutators generated by Calderón–Zygmund operators on generalized Morrey spaces associated with ball Banach function spaces

Implicit iterative algorithms of the split common fixed point problem for Bregman quasi-nonexpansive mapping in Banach spaces

In this paper, we study a modified implicit rule for finding a solution of split common fixed point problem of a Bregman quasi-nonexpansive mapping in Banach spaces. We propose a new iterative algorithm and prove the strong convergence theorem under appropriate conditions. As an applica- tion, the results are applied to solving the zero problem and the equilibrium problem.

Common Attractive Point Theorems for a Finite Family of Multivalued Nonexpansive Mappings in Banach Spaces

OurmainpurposeofthispaperistointroducethemodifiedMannandIshikawaiteratesforfindingacommonattractivepoint of a finite family of multivalued nonexpansive mappings in the setting of uniformly convex Banach spaces. Weobtain necessary and sufficient conditions to guarantee the strong convergence of the proposed algorithms withoutclosedness of the domain of such mappings. Moreover, we derive some consequences from our main result to fixedpoint result of such mappings. Finally, the numerical results are provided to support our main theorem.

Barbashin type characterizations for the uniform polynomial stability and instability of evolution families

Abstract The aim of this paper is to give some discrete and continuous versions of Barbashin type theorems for the uniform polynomial stability and instability of evolution families in Banach spaces, by using Banach sequence spaces in ℋ ⁢ ( ℕ ≥ 1 ) {\mathcal{H}(\mathbb{N}_{\geq 1})} and Banach function spaces in ℋ ⁢ ( ℝ ≥ 1 ) {\mathcal{H}(\mathbb{R}_{\geq 1})} , respectively. Variants for uniform polynomial stability and instability of some well-known results in the exponential stability theory and polynomial stability theory are obtained.

Inequalities and equalities on the joint and generalized spectral and essential spectral radius of the Hadamard geometric mean of bounded sets of positive kernel operators

We prove new inequalities and equalities for the generalized and the joint spectral radius (and their essential versions) of Hadamard (Schur) geometric means of bounded sets of positive kernel operators on Banach function spaces. In the case of non-negative matrices that define operators on Banach sequences, we obtain additional results. Our results extend the results of several authors that appeared relatively recently.

Approximating Fixed Points of Nonexpansive Type Mappings via General Picard–Mann Algorithm

The aim of this paper is to approximate fixed points of nonexpansive type mappings in Banach spaces when the set of fixed points is nonempty. We study the general Picard–Mann (GPM) algorithm, obtaining the weak and strong convergence theorems. We provide an example to illustrate the convergence behaviour of the GPM algorithm. We compare the GPM algorithm with other existing (well known) algorithms numerically (under different parameters and initial guesses).

Approximations of Fixed Point of Nonexpansive Mappings in Banach Spaces

n this paper, we used condition (E) to study approximation on the Banach space, demonstrating the convergence theorem as well as an example that supports the main theorem. Iterative fixed point approximation for nonlinear operators is a novel area of investigation. As a result, the literature contains a number of iterative techniques for overcoming such impediments and improving the rate of convergence.

Fixed Point of Modified F-Contraction with an Application

In this paper, we prove the existence of fixed points for every 2-rotative continuous mapping in Banach spaces to answer an open question raised by Goebel and Koter. Further, we modify F-contraction by developing F-rotative mapping and establish some fixed-point theorems. Finally, we apply our results to prove the existence of a solution of a non-linear fractional differential equation.

Boundedness of Operators and Inequalities on Morrey–Banach Spaces

This paper establishes the boundedness of the spherical maximal function, Rubio de Francia operators, Bochner–Riesz operators, Fourier integral operators, geometric maximal operator, minimal operator and strongly singular integral operators on Morrey spaces built on Banach function spaces. We also establish the Coifman–Fefferman inequalities, Gundy–Wheeden inequalities and Sobolev–Lieb–Thirring inequalities on Morrey–Banach spaces. In particular, our results include the boundedness of the above operators and inequalities on classical Morrey spaces, generalized Morrey spaces, Orlicz–Morrey spaces, Morrey–Lorentz spaces and Morrey spaces with variable exponents.

The order-type Banach-Saks properties

The study of the Banach-Saks property in Banach spaces has a long and illustrious history. Of late, motivated by applications in financial mathematics, interest has arisen in the Banach-Saks type properties with respect to order convergence. This paper presents a study of order Banach-Saks properties in Banach function spaces, and in particular in rearrangement invariant spaces. Among the results obtained, we provide some sufficient conditions for the (weak) order Banach-Saks property. We also characterize the (weak) order Banach-Saks property in Orlicz spaces. It is also shown that the (weak) order Banach-Saks property is equivalent to its hereditary version.

On symmetric $G$-differential and convex functionals in Banach spaces

On symmetric $G$-differential and convex functionals in Banach spaces

On Stević-Sharma Operators from General Class of Analytic Function Spaces into Zygmund-Type Spaces

A Stevi c ′ -Sharma operator denoted by T ψ 1 , ψ 2 , φ is a generalization product of multiplication, differentiation, and composition operators. In this paper, we characterize the bounded and compact Stevi c ′ -Sharma operator T ψ 1 , ψ 2 , φ from a general class X of Banach function spaces into Zygmund-type spaces with some of the most convenient test functions on the open unit disk. Using several restrictive terms, we show that all bounded operators T ψ 1 , ψ 2 , φ from X into the little Zygmund-type spaces are compact. As an application, we show that our results hold up for some other domain spaces of T ψ 1 , ψ 2 , φ , such as the Hardy space and the weighted Bergman space.

The New Iterative Approximating of Endpoints of Multivalued Nonexpansive Mappings in Banach Spaces

The purpose of this paper is to introduce the new iteration process to approximate endpoints of multivalued nonexpansive mappings in Banach space. We prove weak and strong convergence theorems of proposed iterative scheme under some suitable assumptions in the framework of a uniformly convex Banach space.

EXISTENCE AND UNIQUENESS FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH MULTIPOINT AND MULTI-TERM INTEGRAL BOUNDARY CONDITIONS

We investigated the existence and uniqueness of solutions to a nonlinear fractional differential equation containing the Caputo operator supplemented with separated multipoint and multi-term integral boundary conditions. The existence results are obtained by utilizing the Banach contraction principle and the well-known fixed point theorem of Krasnoselskii for a sum of contraction and compact mappings in Banach spaces. Some examples are also presented to illustrate the main results.

ON THE DENSITY OF LAGUERRE FUNCTIONS IN SOME BANACH FUNCTION SPACES

Let λ > 0 and Φλ := {ϕ1,λ, ϕ2,λ, . . . } be the system of dilated Laguerre functions. We show that if L1 (R+) ∩ L∞(R+) is embedded into a separable Banach function space X(R+), then the linear span of Φλ is dense in X(R+). This implies that the linear span of Φλ is dense in every separable rearrangement-invariant space X(R+) and in every separable variable Lebesgue space Lp(·) (R+)

Iterative construction of the fixed point of Suzuki's generalized nonexpansive mappings in Banach spaces

Iterative construction of the fixed point of Suzuki's generalized nonexpansive mappings in Banach spaces

Extrapolation on function and modular spaces, and applications

We generalize the extrapolation theory of Rubio de Francia to the context of Banach function spaces and modular spaces. Our results are formulated in terms of some natural weighted estimates for the Hardy-Littlewood maximal function and are stated in measure spaces and for general Muckenhoupt bases. Finally, we give several applications in analysis and partial differential equations.

Krasnoselskii iteration process for approximating fixed points of enriched generalized nonexpansive mappings in Banach spaces

We consider the class of enriched generalized nonexpansive mappings which includes enriched Kannan mappings, nonexpansive enriched Chatterjea mappings and enriched mappings. We prove some fixed point theorems for enriched generalized nonexpansive mappings using Krasnoselskii iteration process in Banach spaces. We also give stability result for such mappings under some appropriate conditions. The results presented in this paper improve and extend some works in literature.