Some Modified Extragradient Methods for Common Solutions of Generalized Equilibrium Problems and Fixed Points of Nonexpansive Mappings

Abstract

In this paper, we introduce some new iterative schemes based on the extragradient method (and the hybrid method) for finding a common element of the set of solutions of a generalized equilibrium problem, the set of fixed points of a family of nonexpansive mappings, and the set of solutions of the variational inequality for a monotone, Lipschitz continuous mapping in Hilbert spaces. We obtain some strong convergence theorems and weak convergence theorems. The results in this paper generalize, improve and unify some well-known convergence theorems in the literature.