Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 528476, 11 pages
doi:10.1155/2008/528476

Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings

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.