On split generalized equilibrium and fixed point problems with multiple output sets in real Banach spaces

Abstract

In this paper, we propose and study a modified inertial Halpern method for finding a common element of the set of solution of split generalized equilibrium problem which is also a fixed point of Bregman relatively nonexpansive mapping in p-uniformly convex Banach spaces which are also uniformly smooth. Our iterative method uses step-size which does not require prior knowledge of the operator norm and we prove a strong convergence result under some mild conditions. We display a numerical example to illustrate the performance of our result. The result presented in this article unifies and extends several existing results in the literature.