Uamporn Witthayarat

Convergence theorem for equilibrium problem and Bregman strongly nonexpansive mappings in Banach spaces

In this paper, we present an iterative scheme for Bregman strongly nonexpansive mappings in the framework of Banach spaces. Furthermore, we prove the strong convergence theorem for finding common fixed points with the set of solutions of an equilibrium problem.

Hybrid Algorithms of Common Solutions of Generalized Mixed Equilibrium Problems and the Common Variational Inequality Problems with Applications

We introduce new iterative algorithms by hybrid method for finding a common element of the set of solutions of fixed points of infinite family of nonexpansive mappings, the set of common solutions of generalized mixed equilibrium problems, and the set of common solutions of the variational inequality with inverse-strongly monotone mappings in a real Hilbert space. We prove the strong convergence of the proposed iterative method under some suitable conditions. Finally, we apply our results to complementarity problems and optimization problems. Our results improve and extend the results announced by many others.

A viscosity hybrid steepest-descent method for a system of equilibrium and fixed point problems for an infinite family of strictly pseudo-contractive mappings

Based on a viscosity hybrid steepest-descent method, in this paper, we introduce an iterative scheme for finding a common element of a system of equilibrium and fixed point problems of an infinite family of strictly pseudo-contractive mappings which solves the variational inequality 〈(γf−μF)q,p−q〉≤0 for p∈⋂i=1∞F(Ti). Furthermore, we also prove the strong convergence theorems for the proposed iterative scheme and give a numerical example to support and illustrate our main theorem.MSC:46C05, 47D03, 47H05,47H09, 47H10, 47H20.

Convergence of an Iterative Algorithm for Common Solutions for Zeros of Maximal Accretive Operator with Applications

The aim of this paper is to introduce an iterative algorithm for finding a common solution of the sets (A

A New Modified Hybrid Steepest-Descent by Using a Viscosity Approximation Method with a Weakly Contractive Mapping for a System of Equilibrium Problems and Fixed Point Problems with Minimization Problems

The purpose of this paper is to consider a modified hybrid steepest-descent method by using a viscosity approximation method with a weakly contractive mapping for finding the common element of the set of a common fixed point for an infinite family of nonexpansive mappings and the set of solutions of a system of an equilibrium problem. The sequence is generated from an arbitrary initial point which converges in norm to the unique solution of the variational inequality under some suitable conditions in a real Hilbert space. The results presented in this paper generalize and improve the results of Moudafi (2000), Marino and Xu (2006), Tian (2010), Saeidi (2010), and some others. Finally, we give an application to minimization problems and a numerical example which support our main theorem in the last part.

Iterative Scheme for System of Equilibrium Problems and Bregman Asymptotically Quasi-Nonexpansive Mappings in Banach Spaces

Abstract In this paper, we presented a new iterative scheme for finding common fixed points of two Bregman asymptotically quasi-nonexpansive mappings together with the solutions of equilibrium problems in Banach spaces. Furthermore, the convergence theorem and its deduced theorems are also proved and presented. Our results extend and improve the recent ones of some others in the literature.

Modified Iterative Scheme for Multivalued Nonexpansive Mappings, Equilibrium Problems and Fixed Point Problems in Banach Spaces

In this research, we modified iterative scheme for finding common element of the set of fixed point of total quasi-\(\phi \)-asymptotically nonexpansive multivalued mappings, the set of solution of an equilibrium problem and the set of fixed point of relatively nonexpansive mappings in Banach spaces. In addition, the strong convergence for approximating common solution of our mentioned problems is proved under some mild conditions. Our results extend and improve some recent results announced by some authors. We divide our research details into three main sections including Introduction, Preliminaries, Main Results. First, we introduce the backgrounds and motivations of this research and follow with the second section, Preliminaries, which mention about the tools that will be needed to prove our main results. In the last section, Main Results, we propose the theorem and corollary which is the most important part in our research.