Strong convergence of a Bregman projection method for the solution of pseudomonotone equilibrium problems in Banach spaces
Strong convergence of a Bregman projection method for the solution of pseudomonotone equilibrium problems in Banach spaces
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.
Banach space, equilibrium problem, fixed point, quasi-ϕ-nonexpansive mapping, strong convergence, strongly pseudomonotone
69-94
Oyewole, Olawale Kazeem
6e9e09ed-3aeb-4a42-acb3-67d7318288ec
Jolaoso, Lateef Olakunle
102467df-eae0-4692-8668-7f73e8e02546
Aremu, Kazeem Olalekan
7c8766e4-ec45-4093-baca-e79f01088056
2024
Oyewole, Olawale Kazeem
6e9e09ed-3aeb-4a42-acb3-67d7318288ec
Jolaoso, Lateef Olakunle
102467df-eae0-4692-8668-7f73e8e02546
Aremu, Kazeem Olalekan
7c8766e4-ec45-4093-baca-e79f01088056
Oyewole, Olawale Kazeem, Jolaoso, Lateef Olakunle and Aremu, Kazeem Olalekan
(2024)
Strong convergence of a Bregman projection method for the solution of pseudomonotone equilibrium problems in Banach spaces.
Kyungpook Mathematical Journal, 64 (1), .
(doi:10.5666/KMJ.2024.64.1.69).
Abstract
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.
Text
KMJ-21-0292_R2 (1)
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Accepted/In Press date: 7 July 2023
Published date: 2024
Keywords:
Banach space, equilibrium problem, fixed point, quasi-ϕ-nonexpansive mapping, strong convergence, strongly pseudomonotone
Identifiers
Local EPrints ID: 491007
URI: http://eprints.soton.ac.uk/id/eprint/491007
ISSN: 1225-6951
PURE UUID: e8ae9b70-3426-473a-8053-781c2ab02d34
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Date deposited: 11 Jun 2024 16:37
Last modified: 20 Jun 2024 01:59
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Contributors
Author:
Olawale Kazeem Oyewole
Author:
Kazeem Olalekan Aremu
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