EXISTENCE RESULTS FOR NEW GENERALIZED MIXED EQUILIBRIUM AND FIXED POINT PROBLEMS IN BANACH SPACES

Abstract

In this paper, existence and uniqueness results for the solution of a new class of equilibrium problem is established. Using the KKM technique, we establish the existence and uniqueness of solutions of a new generalized mixed equilibrium problem (NGMEP) with trifunctions. Further, we propose an iterative algorithm for finding a common element in the solution set of the NGMEP and a fixed point set of a nonlinear mapping. We proved the strong convergence of the algorithm to a common element in the solution set of a system of NGMEP and a fixed point set of a countable family of totally quasi-φ-asymptotically nonexpansive mapping in the framework of a real uniformly convex and uniformly smooth Banach space. Our result generalize many other results obtained recently in this direction.