Full Text: PDF
Volume 4, Issue 3, 1 December 2022, Pages 349-366
Abstract. 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.
How to Cite this Article:
Olawale Kazeem Oyewole, Simeon Reich, A totally relaxed self-adaptive algorithm for solving a variational inequality and fixed point problems in Banach spaces, Appl. Set-Valued Anal. Optim. 4 (2022), 349-366.