Strong Convergence of A Hybrid Method for Infinite Family of Nonexpansive Mapping and Variational Inequality

The motivation behind this paper is to use hybrid method for searching a typical component of the set of fixed point of an infinite family of non expansive mapping and the set of monotone, Lipschtiz continuous variational inequality problem. The contemplated method is combination of two method one is extragradient method and the other one is DQ method. Also, we demonstrate the strong convergence of the designed iterative technique, under some warm conditions.

Fixed Point Theorems for Generalized θ − ϕ − Expansive Mapping in Rectangular Metric Spaces

In this paper, we present the notion of θ − ϕ − expansive mapping in complete rectangular metric spaces and study various fixed point theorems for such mappings. The presented theorems extend, generalize, and improve many existing results in the literature.

SOME COMMON FIXED POINT THEOR MS FOR EXPANSIVE MAPPINGS IN d-COMPLETE TOPOLOGICAL SPACES

In the present paper, we entrenched common fixed point theorems for self mappings satisfying expansive condition in d-complete topological spaces. Also we prove a fixed point theorem for $(\zeta,\alpha)$-expansive mapping in the setting of d-complete topological spaces. Our results extend and generalize the results of Shahi et al. to d-complete topological spaces.

Fixed Point Results of Expansive Mappings in Metric Spaces

In this study, we introduce the concept of θ-expansive mapping in ordered metric spaces and prove a fixed point theorem for such mappings. We give some fixed point results for θ-expansive mapping in metric spaces and prove fixed point theorems for such mappings. These results extend the main results of many comparable results from the current literature. We also obtain a common fixed point theorem of two weakly compatible mappings in metric spaces. Finally, the examples are presented to support the new theorems and results proved.

Hybrid subgradient algorithm for equilibrium and fixed point problems by approximation of nonexpansive mapping

In this paper anew algorithm considered on a real Hilbert space for finding acommonpoint in the solution set of a class of pseudomonotone equilibrium problem and the set of fixed points of nonexpansive mappings. We produce this algorithm by mappings Tk that are approximations of non-expansive mapping T. The strong convergence theorem of the proposed algorithms is investigated. Our results generalize some recent results in the literature.

Viscosity Approximation Methods for a General Variational Inequality System and Fixed Point Problems in Banach Spaces

In Banach spaces, we study the problem of solving a more general variational inequality system for an asymptotically non-expansive mapping. We give a new viscosity approximation scheme to find a common element. Some strong convergence theorems of the proposed iterative method are obtained. A numerical experiment is given to show the implementation and efficiency of our main theorem. Our results presented in this paper generalize and complement many recent ones.

Convergence of Two Splitting Projection Algorithms in Hilbert Spaces

The aim of this present paper is to study zero points of the sum of two maximally monotone mappings and fixed points of a non-expansive mapping. Two splitting projection algorithms are introduced and investigated for treating the zero and fixed point problems. Possible computational errors are taken into account. Two convergence theorems are obtained and applications are also considered in Hilbert spaces

Convergence of the Ishikawa Type Iteration Process with Errors of I-Asymptotically Quasi-nonexpansive Mappings in Cone Metric Spaces

The goal of this article is to consider an Ishikawa type iteration process with errors to approximate the fixed point of -asymptotically quasi non-expansive mapping in convex cone metric spaces. Our results extend and generalize many known results from complete generalized convex metric spaces to cone metric spaces.