Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 165098, 18 pages
doi:10.1155/2010/165098
Research Article

A New Iterative Method for Solving Equilibrium Problems and Fixed Point Problems for Infinite Family of Nonexpansive Mappings

Shenghua Wang,1 Yeol Je Cho,2 and Xiaolong Qin3

1School of Mathematics and Physics, North China Electric Power University, Baoding 071003, China
2Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea
3Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, China

Received 7 January 2010; Revised 21 May 2010; Accepted 11 July 2010

Academic Editor: Simeon Reich

Copyright © 2010 Shenghua Wang 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 for finding a common element of the solutions sets of a finite family of equilibrium problems and fixed points sets of an infinite family of nonexpansive mappings in a Hilbert space. As an application, we solve a multiobjective optimization problem using the result of this paper.