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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 818970, 14 pages
http://dx.doi.org/10.1155/2012/818970
Research Article

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

Department of Mathematics, Zhejiang Normal University, Zhejiang 321004, China

Received 15 May 2012; Accepted 8 June 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Yuanheng Wang and Liu Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.