An Iterative Method for Mixed Point Problems of Nonexpansive and Monotone Mappings and Generalized Equilibrium Problems

Abstract

In this paper, we introduce an iterative scheme for finding the common element of the set of fixed points of a countable family of nonexpansive mappings, the set of solutions of variational inequality for $\mu$-Lipschitzian, relaxed $(\lambda,\gamma)$-cocoercive mapping and the set of solutions of a generalized equilibrium problem. We show that the iterative sequence converges strongly to a common element of the three sets. Our results generalize many recent results, for example, the results of B. Ali [2].