Abstract and Applied Analysis
Volume 2010 (2010), Article ID 428293, 27 pages
doi:10.1155/2010/428293
Research Article

A New Iterative Method for Finding Common Solutions of a System of Equilibrium Problems, Fixed-Point Problems, and Variational Inequalities

Jian-Wen Peng,1 Soon-Yi Wu,2 and Jen-Chih Yao3

1School of Mathematics, Chongqing Normal University, Chongqing 400047, China
2Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan
3Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan

Received 18 February 2010; Revised 22 May 2010; Accepted 22 June 2010

Academic Editor: Simeon Reich

Copyright © 2010 Jian-Wen Peng et al. 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

We introduce a new iterative scheme based on extragradient method and viscosity approximation method for finding a common element of the solutions set of a system of equilibrium problems, fixed point sets of an infinite family of nonexpansive mappings, and the solution set of a variational inequality for a relaxed cocoercive mapping in a Hilbert space. We prove strong convergence theorem. The results in this paper unify and generalize some well-known results in the literature.