Hybrid iterative scheme by a relaxed extragradient method for solutions of equilibrium problems and a general system of variational inequalities with application to optimization

2009 ◽  
Vol 3 (4) ◽  
pp. 640-656 ◽  
Author(s):  
Wiyada Kumam ◽  
Poom Kumam
Keyword(s):  
Variational Inequalities ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Extragradient Method ◽  
General System ◽  
System Of Variational Inequalities

scholarly journals Hybrid Iterative Scheme by a Relaxed Extragradient Method for Equilibrium Problems, a General System of Variational Inequalities and Fixed-Point Problems of a Countable Family of Nonexpansive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Qiao-Li Dong ◽  
Yan-Ni Guo ◽  
Fang Su
Keyword(s):  
Iterative Method ◽  
Variational Inequalities ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Extragradient Method ◽  
General System ◽  
Countable Family ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
System Of Variational Inequalities

Based on the relaxed extragradient method and viscosity method, we introduce a new iterative method for finding a common element of solution of equilibrium problems, the solution set of a general system of variational inequalities, and the set of fixed points of a countable family of nonexpansive mappings in a real Hilbert space. Furthermore, we prove the strong convergence theorem of the studied iterative method. The results of this paper extend and improve the results of Ceng et al., (2008), W. Kumam and P. Kumam, (2009), Yao et al., (2010) and many others.

scholarly journals Modified Relaxed Extragradient Method for a General System of Variational Inequalities and Nonexpansive Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yuanheng Wang ◽  
Liu Yang
Keyword(s):  
Variational Inequalities ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Extragradient Method ◽  
General System ◽  
Iterative Sequence ◽  
Monotone Mappings ◽  
System Of Variational Inequalities ◽  
Common Solution ◽  
Demiclosedness Principle

The purpose of this paper is to introduce a new modified relaxed extragradient method and study for finding some common solutions for a general system of variational inequalities with inversestrongly monotone mappings and nonexpansive mappings in the framework of real Banach spaces. By using the demiclosedness principle, it is proved that the iterative sequence defined by the relaxed extragradient method converges strongly to a common solution for the system of variational inequalities and nonexpansive mappings under quite mild conditions.

Sign in / Sign up

Export Citation Format

Share Document