Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 95412, 9 pages
A General Iterative Method for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces
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
Academic Editor: Hichem Ben-El-Mechaiekh
Copyright © 2007 Meijuan Shang 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.
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.