Inertial method for a solution of Split Equality of Monotone Inclusion and the $f$-Fixed Point Problems in Banach Spaces

Abstract

In this paper, we propose an inertial algorithm for solving split equality of monotone inclusion and $f$-fixed point of Bregman relatively $f$-nonexpansive mapping problems in reflexive real Banach spaces. Using the Bregman distance function, we prove a strong convergence theorem for the algorithm produced by the method in real reflexive Banach spaces. As an application, we provide several applications of our method. Furthermore, we give a numerical example to demonstrate the behavior of the convergence of the algorithm.