On split generalized equilibrium and fixed point problems of Bregman W-mappings with multiple output sets in reflexive Banach spaces
On split generalized equilibrium and fixed point problems of Bregman W-mappings with multiple output sets in reflexive Banach spaces
In this paper, we introduce a Halpern iteration process for computing the common solution of split generalized equilibrium problem and fixed points of a countable family of Bregman W-mappings with multiple output sets in reflexive Banach spaces. We prove a strong convergence result for approximating the solutions of the aforementioned problems under some mild conditions. It is worth mentioning that the iterative algorithm employ in this article is designed in such a way that it does not require the prior knowledge of operator norm. We also provide some numerical examples to illustrate the performance of our proposed iterative method. The result discuss in this paper extends and complements many related results in literature.
Bregman W-mapping, Bregman weak relatively nonexpansive mapping, Halpern method, iterative scheme, split generalized equilibrium problem
653-672
Abass, Hammed A.
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Ugwunnadi, Godwin C.
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Jolaoso, Lateef O.
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Narain, Ojen K.
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20 October 2023
Abass, Hammed A.
aa6a64a5-79bf-41dd-a5d0-0681fdc1e9ec
Ugwunnadi, Godwin C.
437333ca-cb32-46f2-bf49-1c355dd28db3
Jolaoso, Lateef O.
102467df-eae0-4692-8668-7f73e8e02546
Narain, Ojen K.
3df1bd61-3295-42c2-aeb1-aa4c67f3869a
Abass, Hammed A., Ugwunnadi, Godwin C., Jolaoso, Lateef O. and Narain, Ojen K.
(2023)
On split generalized equilibrium and fixed point problems of Bregman W-mappings with multiple output sets in reflexive Banach spaces.
Mathematical Modelling and Analysis, 28 (4), .
(doi:10.3846/mma.2023.17087).
Abstract
In this paper, we introduce a Halpern iteration process for computing the common solution of split generalized equilibrium problem and fixed points of a countable family of Bregman W-mappings with multiple output sets in reflexive Banach spaces. We prove a strong convergence result for approximating the solutions of the aforementioned problems under some mild conditions. It is worth mentioning that the iterative algorithm employ in this article is designed in such a way that it does not require the prior knowledge of operator norm. We also provide some numerical examples to illustrate the performance of our proposed iterative method. The result discuss in this paper extends and complements many related results in literature.
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17087-Article Text-80438-2-10-20231003
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Accepted/In Press date: 3 October 2023
Published date: 20 October 2023
Additional Information:
Funding Information:
The first author acknowledge with thanks the bursary and financial support from Department of Science and Technology and National Research Foundation, Republic of South Africa Center of Excellence in Mathematical and Statistical Sciences (DSI-NRF COE-MaSS) Post-Doctoral Fellowship. Opinions expressed and conclusions arrived are those of the authors and are not necessarily to be attributed to the CoE-MaSS.
Keywords:
Bregman W-mapping, Bregman weak relatively nonexpansive mapping, Halpern method, iterative scheme, split generalized equilibrium problem
Identifiers
Local EPrints ID: 484932
URI: http://eprints.soton.ac.uk/id/eprint/484932
ISSN: 1392-6292
PURE UUID: 5cb32df2-f51e-4b93-9212-bd283f681805
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Date deposited: 24 Nov 2023 17:40
Last modified: 18 Mar 2024 04:04
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Contributors
Author:
Hammed A. Abass
Author:
Godwin C. Ugwunnadi
Author:
Ojen K. Narain
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