Hybrid Methods for Equilibrium Problems and Fixed Points Problems of a Countable Family of Relatively Nonexpansive Mappings in Banach Spaces

Abstract

The purpose of this paper is to introduce hybrid projection algorithms for finding a common element of the set of common fixed points of a countable family of relatively nonexpansive mappings and the set of solutions of an equilibrium problem in the framework of Banach spaces. Moreover, we apply our result to the problem of finding a common element of an equilibrium problem and the problem of finding a zero of a maximal monotone operator. Our result improve and extend the corresponding results announced by Takahashi andZembayashi 2008 and , and many others.

Strong Convergence Theorem for Equilibrium Problems and Fixed Points of a Nonspreading Mapping in Hilbert Spaces

“…Some methods have been proposed to solve the equilibrium problem and fixed point problem of nonexpansive mapping: see, for instance, 1,2,6,7,[17][18][19][20] and the references Fixed Point Theory and Applications 3 therein. In 1997, Combettes and Hirstoaga 3 introduced an iterative scheme of finding the best approximation to the initial data when EP F is nonempty and proved a strong convergence theorem.…”