Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 362191, 21 pages
doi:10.1155/2009/362191
Research Article

Strong Convergence of an Iterative Method for Equilibrium Problems and Variational Inequality Problems

HongYu Li1 and HongZhi Li2

1Department of Mathematics, TianJin Polytechnic University, TianJin 300160, China
2Department of Mathematics, Agricultural University of Hebei, BaoDing 071001, China

Received 26 August 2008; Revised 11 November 2008; Accepted 9 January 2009

Academic Editor: Massimo Furi

Copyright © 2009 HongYu Li and HongZhi Li. 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 method for finding a common element of the set of solutions of equilibrium problems, the set of solutions of variational inequality problems, and the set of fixed points of finite many nonexpansive mappings. We prove strong convergence of the iterative sequence generated by the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for the minimization problem.