Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 64363, 12 pages
doi:10.1155/2007/64363
Research Article
Convergence Theorem for Equilibrium Problems and Fixed Point Problems of Infinite Family of Nonexpansive Mappings
1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
2Department of Information Management, Cheng Shiu University, Kaohsiung 833, Taiwan
3Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 804, Taiwan
Received 17 March 2007; Accepted 20 August 2007
Academic Editor: Billy E. Rhoades
Copyright © 2007 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
We introduce an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of infinite nonexpansive mappings in a Hilbert space. We prove a strong-convergence theorem under mild assumptions on parameters.