A New Hybrid Iterative Method for Solving Mixed Equilibrium and Fixed Point Problems for Bregman Relatively Nonexpansive Mappings

Abstract

In this paper, we introduce a new hybrid iterative method for finding a common solution of a mixed equilibrium problem and a fixed point problem for a Bregman relatively nonexpansive mapping in reflexive Banach spaces. We prove that a sequence generated by the hybrid iterative algorithm converges strongly to a common solution of these problems. Finally, we provide some consequences of the main result and give a numerical example to demonstrate the applicability of the iterative algorithm.