Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 528476, 11 pages
doi:10.1155/2008/528476
Research Article
Strong Convergence Theorem by a New Hybrid Method for Equilibrium Problems and Relatively Nonexpansive Mappings
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, Japan
Received 6 September 2007; Accepted 8 January 2008
Academic Editor: Simeon Reich
Copyright © 2008 Wataru Takahashi and Kei Zembayashi. 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 prove a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a relatively nonexpansive mapping in a Banach space by using a new hybrid method. Using this theorem, we obtain two new results for finding a solution of an equilibrium problem and a fixed point of a relatively nonexpnasive mapping in a Banach space.