SOME NEW ITERATIVE ALGORITHMS FOR GENERALIZED MIXED EQUILIBRIUM PROBLEMS WITH STRICT PSEUDO-CONTRACTIONS AND MONOTONE MAPPINGS

Abstract

In this paper, we propose some parallel and cyclic algorithms based on the extragradient method (nonextragradient method) for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of fixed points of a finite family of strict pseudo-contractions and the set of the variational inequality for a monotone, Lipschitz continuous mapping (an inverse strongly monotone mapping). We obtain some weak and strong convergence theorems for the sequences generated by these processes in Hilbert spaces. The results in this paper generalize, improve and unify some well-known results in the literature.