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

Wataru Takahashi and Kei Zembayashi

 Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, Japan
Received 6 September 2007; Accepted 8 January 2008

Recommended by Simeon Reich

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.