Article
Kyungpook Mathematical Journal 2024; 64(1): 69-94
Published online March 31, 2024
Copyright © Kyungpook Mathematical Journal.
Strong Convergence of a Bregman Projection Method for the Solution of Pseudomonotone Equilibrium Problems in Banach Spaces
Olawale Kazeem Oyewole∗, Lateef Olakunle Jolaoso, Kazeem Olalekan Aremu
The Technion – Israel Institute of Technology, 32000 Haifa, Israel
e-mail : oyewoleolawalekazeem@gmail.com, oyewoleok@campus.technion.ac.il
School of Mathematics, University of Southampton, SO171 BJ, United Kingdom Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences, P. O. Box 94 Medunsa 0204, Ga-Rankuwa, South Africa
e-mail : jollatanu@yahoo.co.u
Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences, P. O. Box 94 Medunsa 0204, Ga-Rankuwa, South Africa School of Mathematics, Usmanu Danfodiyo University Sokoto, P. M. B. 2346, Sokoto, Sokoto State, Nigeria
e-mail : aremu.kazeem@udusok.edu.ng, aremukazeemolalekan@gmail.com
Received: November 1, 2021; Revised: October 5, 2022; Accepted: November 15, 2022
In this paper, we introduce an inertial self-adaptive projection method using Bregman distance techniques for solving pseudomonotone equilibrium problems in reflexive Banach spaces. The algorithm requires only one projection onto the feasible set without any Lipschitz-like condition on the bifunction. Using this method, a strong convergence theorem is proved under some mild conditions. Furthermore, we include numerical experiments to illustrate the behaviour of the new algorithm with respect to the Bregman function and other algorithms in the literature.
Keywords: equilibrium problem, strongly pseudomonotone, strong convergence, Banach space, quasi-ϕ-nonexpansive mapping, fixed point