A totally relaxed self-adaptive algorithm for solving a variational inequality and fixed point problems in Banach spaces
Applied Set-Valued Analysis and Optimization · 2022
Using the Halpern iterative method, we propose and study a totally relaxed iterative algorithm for approximating a common solution to variational inequality and fixed point problems in certain Banach space.Our algorithm uses a self-adaptive step size to avoid the dependence on the Lipschitz constant of the operator involved.Our method can also find fixed points of Bregman firmly nonexpansive mappings.We establish a strong convergence theorem and present some numerical experiments to illustrate the performance of our algorithm.