Abstract and Applied Analysis
Volume 2010 (2010), Article ID 763506, 19 pages
doi:10.1155/2010/763506
Research Article

Composite Algorithms for Minimization over the Solutions of Equilibrium Problems and Fixed Point Problems

Yonghong Yao1 and Yeong-Cheng Liou2

1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
2Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan

Received 7 July 2010; Accepted 27 September 2010

Academic Editor: Chaitan Gupta

Copyright © 2010 Yonghong Yao and Yeong-Cheng Liou. 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 solve the minimization problem of finding x∗ such that x∗=argminx∈Γ‖x‖2, where Γ stands for the intersection set of the solution set of the equilibrium problem and the fixed points set of a nonexpansive mapping. We first present two new composite algorithms (one implicit and one explicit). Further, we prove that the proposed composite algorithms converge strongly to x∗.