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

Kanikar Muangchoo, Poom Kumam, Yeol Je Cho, Sakulbuth Ekvittayaniphon, Wachirapong Jirakitpuwapat

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.