TY - JOUR
T1 - Strong Convergence of a Bregman Projection Method for the Solution of Pseudomonotone Equilibrium Problems in Banach Spaces
AU - Oyewole, Olawale Kazeem
AU - Jolaoso, Lateef Olakunle
AU - Aremu, Kazeem Olalekan
N1 - Publisher Copyright:
© (2024) Kyungpook Mathematical Journal
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
KW - Banach space
KW - equilibrium problem
KW - fixed point
KW - quasi-ϕ-nonexpansive mapping
KW - strong convergence
KW - strongly pseudomonotone
UR - http://www.scopus.com/inward/record.url?scp=85190893870&partnerID=8YFLogxK
U2 - 10.5666/KMJ.2024.64.1.69
DO - 10.5666/KMJ.2024.64.1.69
M3 - Article
AN - SCOPUS:85190893870
SN - 1225-6951
VL - 64
SP - 69
EP - 94
JO - Kyungpook Mathematical Journal
JF - Kyungpook Mathematical Journal
IS - 1
ER -