Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 632819, 15 pages
doi:10.1155/2009/632819
An extragradient method for mixed equilibrium problems and fixed point problems
Yonghong Yao1
, Yeong-Cheng Liou2
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
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.