A new iterative scheme for equilibrium problems, fixed point problems for nonexpansive mappings and zero points of maximal monotone operators

Abstract

In this article, we introduce a new iterative scheme for finding a common element of the set of fixed points of strongly relatively nonexpansive mapping, the set of solutions for equilibrium problems and the set of zero points of maximal monotone operators in a uniformly smooth and uniformly convex Banach space. Consequently, we obtain new strong convergence theorems in the frame work of Banach spaces. Our theorems extend and improve the recent results of Wei et al., Takahashi and Zembayashi, and some recent results. © 2012 Onjai-uea and Kumam.