Nonexpansive Mappings In Banach Spaces Research Articles

Demiclosed principle and some fixed-point theorems for generalized nonexpansive mappings in Banach spaces

The aim of this paper is to discuss some results concerning the demiclosedness principle of generalized, nonexpansive mappings in uniformly convex spaces. Further, we present some new fixed-point theorems for generalized nonexpansive mappings in different settings of Banach spaces.

Strong Convergence Theorems for Split Common Fixed Point Problem of Bregman Generalized Asymptotically Nonexpansive Mappings in Banach Spaces

In this paper, a new iterative scheme is introduced and also strong convergence theorems for solving split common fixed point problem for uniformly continuous Bregman generalized asymptotically nonexpansive mappings in uniformly convex and uniformly smooth Banach spaces are presented. The results are proved without the assumption of semicompactness property and or Opial condition

A new hybrid Halpern-based extragradient algorithm for a pseudomonotone equilibrium problem and a fixed point problem of nonexpansive mappings in Banach spaces

A new hybrid Halpern-based extragradient algorithm for a pseudomonotone equilibrium problem and a fixed point problem of nonexpansive mappings in Banach spaces

Approximation of fixed points for a new class of generalized non-expansive mappings in Banach spaces

<abstract><p>In this paper, we first introduced a new class of generalized non-expansive mappings, which was larger than the class satisfying the condition $ B_{\gamma, \mu } $. Also, we proposed a new iterative process to approximate the fixed point of the mapping we introduced in this work, then we prove convergence theorems for these mappings by using our iteration process. Lastly, a numerical example was given to show the efficiency of this new iteration process. Our results were the extension and generalization of many known results in the literature in fixed point theory.</p></abstract>

Fixed point theorems for suzuki nonexpansive mappings in banach spaces

In this paper, we investigate the existence of fixed points for Suzuki nonexpansive mappings in the setting of Banach spaces using the asymptotic center technique. We also establish the convergence of regular approximate fixed point sequence to the fixed points of Suzuki nonexpansive mappings. Examples are also given to illustrate the results. Our theorems generalize several results in the literature.

Some convergence results using a new iteration process for generalized nonexpansive mappings in Banach spaces

In this paper, we introduce a new iterative process for approximation fixed points. We show the stability of our proposed iteration process. We prove some weak and strong convergence theorems for generalized [Formula: see text]-nonexpansive mappings in the framework of uniformly convex Banach spaces. We also provide an example of a generalized [Formula: see text]-nonexpansive mapping to show numerically that our iteration is faster than various prominent iteration processes.

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.

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.

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.

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

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.

Some fixed point theorems for generalized enriched nonexpansive mappings in Banach spaces

Some fixed point theorems for generalized enriched nonexpansive mappings in Banach spaces

An inertial iterative algorithm for generalized equilibrium problems and Bregman relatively nonexpansive mappings in Banach spaces

The aim of this paper is to introduce and study an inertial hybrid iterative method for solving generalized equilibrium problems involving Bregman relatively nonexpansive mappings in Banach spaces. We study the strong convergence for the proposed algorithm. Finally, we list some consequences and computational example to emphasize the efficiency and relevancy of main result.

On the convergence of an iterative process for enriched Suzuki nonexpansive mappings in Banach spaces

<abstract><p>We study the existence and approximation of fixed points for the recently introduced class of mappings called enriched Suzuki nonexpansive mappings in the setting of Banach spaces. We use the modified $ K $-iteration process to establish the main results of the paper. The class of enriched Suzuki nonexpansive operators is an important class of nonlinear operators that includes properly the class of Suzuki nonexpansive operators as well as enriched nonexpansive operators. Various assumptions are imposed on the domain or on the operator to establish the main convergence theorems. Eventually, a numerical example of enriched Suzuki nonexpansive operators is used to show the effectiveness of the studied iteration scheme. The main outcome of the paper is new and essentially suggests a new direction for researchers who are working on fixed point problems in a Banach space setting. Our results improve and extend some main results due to Hussain et al. (<italic>J. Nonlinear Convex Anal.</italic> 2018, <italic>19</italic>, 1383–1393.), Ullah et al. (<italic>Axioms</italic> 2022, 1.) and others.</p></abstract>

Hybrid subgradient method for pseudomonotone equilibrium problem and fixed points of relatively nonexpansive mappings in Banach spaces

In this paper, we propose a new hybrid subgradient algorithm for finding a common point in the set of solutions of pseudomonotone equilibrium problem and the set of fixed points of relatively nonexpansive mapping in a real uniformly convex and uniformly smooth Banach spaces. Weak and strong convergence of the iterative scheme are established. Our results generalizes and improves several recent results in the literature.

Convergence of SP-Iterations for Generalized Nonexpansive Mappings in Banach Spaces

Convergence of SP-Iterations for Generalized Nonexpansive Mappings in Banach Spaces

Some strong convergence results for two asymptotically quasi G-$$\phi $$-nonexpansive mappings in Banach spaces with directed graphs

Some strong convergence results for two asymptotically quasi G-$$\phi $$-nonexpansive mappings in Banach spaces with directed graphs

Fixed Point Results on Multi-Valued Generalized (α,β)-Nonexpansive Mappings in Banach Spaces

In this paper, we provide and study the concept of multi-valued generalized (α,β)-nonexpansive mappings, which is the multi-valued version of the recently developed generalized (α,β)-nonexpansive mappings. We establish some elementary properties and fixed point existence results for these mappings. Moreover, a multi-valued version of the M-iterative scheme is proposed for approximating fixed points of these mappings in the weak and strong senses. Using an example, we also show that M-iterative scheme converges faster as compared to many other schemes for this class of mappings.

Some properties of generalized fundamentally nonexpansive mappings in Banach spaces

In this paper, we introduce a condition on mappings and show that the class of these mappings is broader than both the class of mappings satisfying condition (C) and the class of fundamentally nonexpansive mappings, and it is incomparable with the class of quasi-nonexpansive mappings and the class of mappings satisfying condition (L). Furthermore, we present some convergence theorems and fixed point theorems for mappings satisfying the condition in the setting of Banach spaces. Finally, an example is given to support the usefulness of our results.

A Convergence Theorem for Solving Generalized Mixed Equilibrium Problems and Finding Fixed Points of a Weak Bregman Relatively Nonexpansive Mappings in Banach Spaces

A Convergence Theorem for Solving Generalized Mixed Equilibrium Problems and Finding Fixed Points of a Weak Bregman Relatively Nonexpansive Mappings in Banach Spaces