Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 392741, 24 pages
doi:10.1155/2011/392741
Research Article

Strong Convergence of a New Iterative Method for Infinite Family of Generalized Equilibrium and Fixed-Point Problems of Nonexpansive Mappings in Hilbert Spaces

Shenghua Wang1,2 and Baohua Guo1,2

1National Engineering Laboratory for Biomass Power Generation Equipment, North China Electric Power University, Baoding 071003, China
2Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, China

Received 15 October 2010; Accepted 18 November 2010

Academic Editor: Qamrul Hasan Ansari

Copyright © 2011 Shenghua Wang and Baohua Guo. 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 an iterative algorithm for finding a common element of the set of solutions of an infinite family of equilibrium problems and the set of fixed points of a finite family of nonexpansive mappings in a Hilbert space. We prove some strong convergence theorems for the proposed iterative scheme to a fixed point of the family of nonexpansive mappings, which is the unique solution of a variational inequality. As an application, we use the result of this paper to solve a multiobjective optimization problem. Our result extends and improves the ones of Colao et al. (2008) and some others.