RELAXED EXTRAGRADIENT-LIKE METHOD FOR GENERAL SYSTEM OF GENERALIZED MIXED EQUILIBRIA AND FIXED POINT PROBLEM

Abstract

In this paper, we introduce two iterative algorithms based on the relaxed extragradient-like method for finding a common element of the solution set of a general system of generalized mixed equilibria and the fixed point set of a strictly pseudocontractive mapping in a real Hilbert space. We will prove the weak convergence of the iterative algorithm under some mild conditions, while the strong convergence is obtained under some more restrictive conditions.