On split feasibility problem for finite families of equilibrium and fixed point problems in Banach spaces
Abstract: In this article, motivated by the works of Ali Akbar and Elahe Shahrosvand [Split equality common null point problem for Bregman quasi-nonexpansive mappings, Filomat 32 (2018), no. 11, 3917–3932], Eskandani et al. [A hybrid extragradient method for solving pseudomonotone equilibrium problem using Bregman distance, J. Fixed Point Theory Appl. 20 (2018), 132], B. Ali and M. H. Harbau [Convergence theorems for Bregman K-mappings and mixed equilibrium problems in reflexive Banach spaces, J. Funct. Spaces (2016) Article ID 5161682, 18 pages], and some other related results in the literature, we introduce a hybrid extragradient iterative algorithm that employs a Bregman distance approach for approximating a split feasibility problem for a finite family of equilibrium problems involving pseudomonotone bifunctions and fixed point problems for a finite family of Bregman quasi-asymptotically nonexpansive mappings using the concept of Bregman K-mapping in reflexive Banach spaces. Using our iterative algorithm, we state and prove a strong convergence result for approximating a common solution to the aforementioned problems. Furthermore, we give an application of our main result to variational inequalities and also report a numerical example to illustrate the convergence of our method. The result presented in this article extends and complements many related results in the literature.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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On split feasibility problem for finite families of equilibrium and fixed point problems in Banach spaces ; volume:55 ; number:1 ; year:2022 ; pages:658-675 ; extent:18
Demonstratio mathematica ; 55, Heft 1 (2022), 658-675 (gesamt 18)
- Creator
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Abass, Hammed A.
Oyewole, Olawale K.
Mebawondu, Akindele A.
Aremu, Kazeem O.
Narain, Ojen K.
- DOI
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10.1515/dema-2022-0158
- URN
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urn:nbn:de:101:1-2022100514253244102605
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:26 AM CEST
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Associated
- Abass, Hammed A.
- Oyewole, Olawale K.
- Mebawondu, Akindele A.
- Aremu, Kazeem O.
- Narain, Ojen K.
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