Strong convergence theorems of iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems
In this paper, a new iterative scheme based on the extragradient method for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a family of finitely nonexpansive mappings and the set of solutions of the variational inequality for a monotone, Lipschitz continuous mapping is proposed. A strong convergence theorem for this iterative scheme in Hilbert spaces is established. Applications to optimization problems are given. (C) 2009 Elsevier Ltd. All rights reserved.
strong convergence extragradient method mixed equilibrium problem fixed point nonexpansive mapping variational inequality monotone mapping