A New Implicit Hybrid Algorithm for an Equilibrium Problem and a Countable Family of Relatively Nonexpansive Mappings in Banach Spaces

Hafiz Fukhar-ud-din, Muhammad Aqeel Ahmad Khan

Abstract

In this paper, we introduce a new implicit shrinking algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a countable family of relatively nonexpansive mappings in the framework of Banach spaces. Our results are refinement as well as generalization of several well-known results in the current literature. As a consequence, we give some applications for solving variational inequality problems and convex minimization problems in Banach spaces.