scholarly journals An Iterative Method with Norm Convergence for a Class of Generalized Equilibrium Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Haixia Zhang ◽  
Fenghui Wang
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Monotone Mappings ◽  
Norm Convergence ◽  
Inverse Strongly Monotone ◽  
Generalized Equilibrium ◽  
Strongly Monotone Mappings

Recently, Takahashi and Takahashi proposed an iterative algorithm for solving a problem for finding common solutions of generalized equilibrium problems governed by inverse strongly monotone mappings and of fixed point problems for nonexpansive mappings. In this paper, we provide a result that allows for the removal of one condition ensuring the strong convergence of the algorithm.

scholarly journals Iterative Methods of Weak and Strong Convergence Theorems for the Split Common Solution of the Feasibility Problems, Generalized Equilibrium Problems, and Fixed Point Problems

2020 ◽  
Vol 2020 ◽  
pp. 1-22
Author(s):  
Shahram Rezapour ◽  
Yuanheng Wang ◽  
Seyyed Hasan Zakeri
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Equilibrium Points ◽  
Fixed Point Problems ◽  
Weak And Strong Convergence ◽  
Iterative Approximation ◽  
Common Solution ◽  
Generalized Equilibrium

The purpose of this paper is to introduce the extragradient methods for solving split feasibility problems, generalized equilibrium problems, and fixed point problems involved in nonexpansive mappings and pseudocontractive mappings. We establish the results of weak and strong convergence under appropriate conditions. As applications of our three main theorems, when the mappings and their domains take different types of cases, we can obtain nine iterative approximation theorems and corollas on fixed points, variational inequality solutions, and equilibrium points.

An Iterative Method for Equilibrium Problems and Fixed Point Problems

2014 ◽  
Vol 513-517 ◽  
pp. 382-385
Author(s):  
Chen Min ◽  
Qiao Hong Jiang
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Strong Convergence ◽  
Fixed Points ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Fixed Point Problems ◽  
Common Element ◽  
Mixed Equilibrium Problems

In this paper, we prove the strong convergence of an iterative method for finding a common element of the set of solutions of mixed equilibrium problems and the set of fixed points of a finite family of nonexpansive mappings under some suitable conditions. Result presented in this paper improves and extends the recent known results in this area.

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

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Monairah Alansari ◽  
Mohammad Farid ◽  
Rehan Ali
Keyword(s):  
Iterative Method ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Iterative Algorithm ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive ◽  
Generalized Equilibrium ◽  
Hybrid Iterative Method

AbstractThe 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.

scholarly journals Iterative Algorithms for Systems of Generalized Equilibrium Problems with the Constraints of Variational Inclusion and Fixed Point Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-24 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Abdul Latif ◽  
Abdullah E. Al-Mazrooei
Keyword(s):  
Fixed Point ◽  
Equilibrium Problems ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Generalized Mixed Equilibrium Problem ◽  
Monotone Mappings ◽  
Point Problem ◽  
Common Solution ◽  
Generalized Equilibrium

We introduce and analyze a hybrid extragradient-like viscosity iterative algorithm for finding a common solution of a systems of generalized equilibrium problems and a generalized mixed equilibrium problem with the constraints of two problems: a finite family of variational inclusions for maximal monotone and inverse strongly monotone mappings and a fixed point problem of infinitely many nonexpansive mappings in a real Hilbert space. Under some suitable conditions, we prove the strong convergence of the sequence generated by the proposed algorithm to a common solution of these problems.

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