Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 632819, 15 pages
doi:10.1155/2009/632819
Research Article

An Extragradient Method for Mixed Equilibrium Problems and Fixed Point Problems

Yonghong Yao,1 Yeong-Cheng Liou,2 and Yuh-Jenn Wu3

1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
2Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan
3Department of Applied Mathematics, Chung Yuan Christian University, Chung Li 320, Taiwan

Received 2 November 2008; Revised 8 April 2009; Accepted 23 May 2009

Academic Editor: Nan-Jing Huang

Copyright © 2009 Yonghong Yao 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

The purpose of this paper is to investigate the problem of approximating a common element of the set of fixed points of a demicontractive mapping and the set of solutions of a mixed equilibrium problem. First, we propose an extragradient method for solving the mixed equilibrium problems and the fixed point problems. Subsequently, we prove the strong convergence of the proposed algorithm under some mild assumptions.