A two-step iterative algorithm for nding common xed point of Bregman quasi strict pseudo-contraction mappings with applications

Abstract

Motivated by some results of authors in this direction, our purpose in this paper is to construct a two-step iterative algorithm with inertial extrapolation term defined with respect to Bregman distance function for approximating common fixed points of a finite family of a closed Bregman quasi strictly pseudo-contraction mappings when the intersection of its set is assumed to be non empty. We prove a strong convergence theorem for it under flexible and relaxed conditions in real reflexive Banach space. Our algorithm is applied in solving finite convex feasibility and equilibrium problems in reflexive Banach space. Furthermore, we demonstrate numerical examples to justify the efficiency and implementability of our algorithms in a finite dimensional real Banach space. Our results improves, generalizes and complements other previously and recently cited results of some authors in the literature of our procedure. It is intended that our procedure complement our motivated result cited in the literature.