Shrinking Projection Method of Common Solutions for Generalized Equilibrium Quasi-ϕ-Nonexpansive Mapping and Relatively Nonexpansive Mapping

Abstract

We prove a strong convergence theorem for finding a common element of the set of solutions for generalized equilibrium problems, the set of fixed points of a relatively nonexpansive mapping, and the set of fixed points of a quasi-ϕ-nonexpansive mapping in a Banach space by using the shrinking Projection method. Our results improve the main results in S. Takahashi and W. Takahashi (2008) and Takahashi and Zembayashi (2008). Moreover, the method of proof adopted in the paper is different from that of S. Takahashi and W. Zembayashi (2008).