On split generalized equilibrium and fixed point problems with multiple output sets in real Banach spaces
On split generalized equilibrium and fixed point problems with multiple output sets in real Banach spaces
In this paper, we propose and study a modified inertial Halpern method for finding a common element of the set of solution of split generalized equilibrium problem which is also a fixed point of Bregman relatively nonexpansive mapping in p-uniformly convex Banach spaces which are also uniformly smooth. Our iterative method uses step-size which does not require prior knowledge of the operator norm and we prove a strong convergence result under some mild conditions. We display a numerical example to illustrate the performance of our result. The result presented in this article unifies and extends several existing results in the literature.
Bregman relatively nonexpansive mapping, Fixed point problem, Generalized equilibrium problem, Inertial method, Resolvent operators
Abass, H. A.
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Oyewole, O. K.
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Narain, O. K.
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Jolaoso, L. O.
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Olajuwon, B. I.
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1 December 2022
Abass, H. A.
2647ac82-5bc5-4624-9726-46e40f07b071
Oyewole, O. K.
887b9e09-a4a3-4df9-9572-c2d19f1a6118
Narain, O. K.
b3a1ac8f-8955-4c69-bb2a-ca43df375c17
Jolaoso, L. O.
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Olajuwon, B. I.
d9c946e9-836c-40cd-9cc9-e593988c1b15
Abass, H. A., Oyewole, O. K., Narain, O. K., Jolaoso, L. O. and Olajuwon, B. I.
(2022)
On split generalized equilibrium and fixed point problems with multiple output sets in real Banach spaces.
Computational and Applied Mathematics, 41 (8), [416].
(doi:10.1007/s40314-022-02136-2).
Abstract
In this paper, we propose and study a modified inertial Halpern method for finding a common element of the set of solution of split generalized equilibrium problem which is also a fixed point of Bregman relatively nonexpansive mapping in p-uniformly convex Banach spaces which are also uniformly smooth. Our iterative method uses step-size which does not require prior knowledge of the operator norm and we prove a strong convergence result under some mild conditions. We display a numerical example to illustrate the performance of our result. The result presented in this article unifies and extends several existing results in the literature.
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Accepted/In Press date: 20 November 2022
e-pub ahead of print date: 29 November 2022
Published date: 1 December 2022
Keywords:
Bregman relatively nonexpansive mapping, Fixed point problem, Generalized equilibrium problem, Inertial method, Resolvent operators
Identifiers
Local EPrints ID: 474280
URI: http://eprints.soton.ac.uk/id/eprint/474280
ISSN: 2238-3603
PURE UUID: 61fd8f71-4997-4099-ae2b-76eab0863044
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Date deposited: 17 Feb 2023 17:30
Last modified: 17 Mar 2024 07:37
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Contributors
Author:
H. A. Abass
Author:
O. K. Oyewole
Author:
O. K. Narain
Author:
B. I. Olajuwon
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