Fixed Point Theory and Applications 
Volume 2007 (2007), Article ID 95412, 9 pages
doi:10.1155/2007/95412
Research Article

A General Iterative Method for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

Meijuan Shang,1,2 Yongfu Su,1 and Xiaolong Qin3

 1Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China
2Department of Mathematics, Shijiazhuang University, Shijiazhuang 050035, China
3Department of Mathematics, Gyeongsang National University, Chinju 660-701, Korea
Received 14 May 2007; Revised 15 August 2007; Accepted 18 September 2007

Recommended by Hichem Ben-El-Mechaiekh

Abstract

We introduce a general iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Our results improve and extend the corresponding ones announced by S. Takahashi and W. Takahashi in 2007, Marino and Xu in 2006, Combettes and Hirstoaga in 2005, and many others.