Strong convergence theorem of a new modified Bregman extragradient method to solve fixed point problems and variational inequality problems in general reflexive Banach spaces

Abstract

In this paper, we introduce a new modified self-adaptive extragradient method with the inertial technique for solving the variational inequality problem of a pseudomonotone mapping and the fixed point problem of a Bregman relatively nonexpansive operator in a general reflexive Banach space. We prove a strong convergence theorem of our algorithm under some suitable assumptions. Finally, some numerical experiments are provided to demonstrate the effectiveness of the suggested iterative method.