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

Olawale Kazeem Oyewole, Oluwatosin Temitope Mewomo

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.



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ISSN: 1229-1595 (Print), 2466-0973 (Online)