STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEMS, FIXED POINT PROBLEMS OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS AND A GENERAL SYSTEM OF VARIATIONAL INEQUALITIES

Abstract

In this paper, we introduce a new iterative scheme for finding the common element of the set of fixed points of an asymptotically nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of a general system of variational inequalities for inverse-strongly monotone mappings in Hilbert spaces. We prove that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. This main result improve and extend the corresponding results announced by many others. Using this theorem, we obtain three corollaries.