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

Yonghong Yao,1 Yeong-Cheng Liou,2 and Jen-Chih Yao3

 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

Recommended by Billy E. Rhoades

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.