Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 531308, 20 pages
doi:10.1155/2009/531308
Research Article

An Iterative Method for Generalized Equilibrium Problems, Fixed Point Problems and Variational Inequality Problems

Qing-you Liu,1 Wei-you Zeng,2 and Nan-jing Huang2

1State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, Sichuan 610500, China
2Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China

Received 11 January 2009; Accepted 28 May 2009

Academic Editor: Fabio Zanolin

Copyright © 2009 Qing-you Liu 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 an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of generalized equilibrium problems, the set of common fixed points of infinitely many nonexpansive mappings, and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in Hilbert spaces. We give some strong-convergence theorems under mild assumptions on parameters. The results presented in this paper improve and generalize the main result of Yao et al. (2007).