Linesearch Methods for Equilibrium Problems and an Infinite Family of Nonexpansive Mappings

Abstract

In this paper, we propose new projection methods for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the solution set of a pseudomonotone equilibrium problem. The iterative schemes are based on the extended extragradient methods, fixed point methods, and Armijo-type linesearch techniques. We show that all of the iterative sequences generated by the scheme converge to the common element under mild assumptions on parameters.