A hybrid method for a countable family of lipschitz generalized asymptotically quasi-nonexpansive mappings and an equilibrium problem

Abstract

In this paper, we introduce a new iterative scheme for finding a common element of the fixed points set of a countable family of uni-formly Lipschitzian generalized asymptotically quasi-nonexpansive map-pings and the solutions set of equilibrium problems. Some strong con-vergence theorems of the proposed iterative scheme are established by using the concept of W-mappings of a countable family of uniformly Lip-schitzian generalized asymptotically quasi-nonexpansive mappings. © 2013 The Korean Mathematical Society.