Viscosity iteration method for generalized equilibrium problems and fixed point problems of finite family of nonexpansive mappings

2012 ◽  
Vol 219 (6) ◽  
pp. 2949-2959 ◽  
Author(s):  
Issara Inchan
Keyword(s):  
Fixed Point ◽  
Iteration Method ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Fixed Point Problems ◽  
Generalized Equilibrium

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.

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