A Modified Method with Inertial-type for Solving Fixed Point and Variational Inequalities Problems in Reflexive Banach Spaces

In this paper, using Bregman distance technique, we introduce an inertial type algorithm with self - adaptive step size for approximating a common element of the set of solutions of pseudomonotone variational inequality problem and the set of common fixed point of a finite family of generic generalized Bregman nonspreading mapping in a real reflexive Banach space. Furthermore, we prove a strong convergence theorem of our algorithm without prior knowledge of the Lipschitz constant of the operator under some mild assumptions. We also give a numerical example to illustrate the performance of our algorithm. Our result generalize and improve many existing results in the literature.