Strong convergence theorem for fixed points of relatively nonexpansive multi-valued mappings and equilibrium problems in Banach spaces

Abstract

In this paper, we study the problem of finding a common element of the solution set of monotone equilibrium problem and the fixed point set of relatively nonexpansive multi-valued mappings in uniformly convex and uniformly smooth Banach spaces. We introduce a Halpern-S-iteration for solving the problem and establish a strong convergence theorem. Some consequences and applications of our main results are discussed. Some numerical experiments are performed to illustrate the convergence and computational performance of our algorithm in comparison with others having similar features. The numerical results have confirmed that the proposed algorithm has a competitive advantage over the existing methods. Our results extend and generalize some results in the literature in this direction.