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A strongly convergent algorithm for solving multiple set split equality equilibrium and fixed point problems in Banach spaces

Part of: Existence theories Nonlinear operators and their properties

Published online by Cambridge University Press:  15 June 2023

E.C. Godwin ,
O.T. Mewomo  and
T.O. Alakoya
E.C. Godwin
Affiliation:
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa (220100908@stu.ukzn.ac.za; emmysworld05@yahoo.com; mewomoo@ukzn.ac.za; alakoyat1@ukzn.ac.za; timimaths@gmail.com)
O.T. Mewomo
Affiliation:
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa (220100908@stu.ukzn.ac.za; emmysworld05@yahoo.com; mewomoo@ukzn.ac.za; alakoyat1@ukzn.ac.za; timimaths@gmail.com)
T.O. Alakoya
Affiliation:
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa (220100908@stu.ukzn.ac.za; emmysworld05@yahoo.com; mewomoo@ukzn.ac.za; alakoyat1@ukzn.ac.za; timimaths@gmail.com)
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Abstract

In this article, using an Halpern extragradient method, we study a new iterative scheme for finding a common element of the set of solutions of multiple set split equality equilibrium problems consisting of pseudomonotone bifunctions and the set of fixed points for two finite families of Bregman quasi-nonexpansive mappings in the framework of p-uniformly convex Banach spaces, which are also uniformly smooth. For this purpose, we design an algorithm so that it does not depend on prior estimates of the Lipschitz-type constants for the pseudomonotone bifunctions. Furthermore, we present an application of our study for finding a common element of the set of solutions of multiple set split equality variational inequality problems and fixed point sets for two finite families of Bregman quasi-nonexpansive mappings. Finally, we conclude with two numerical experiments to support our proposed algorithm.

Keywords

split feasibility problemequilibrium problemfixed-point problempseudomonotone bifunctionp-uniformly convexBregman distancequasi-nonexpansive mappingstrong convergenceBanach spaces

MSC classification

Primary: 47H09: Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc. 47H10: Fixed-point theorems 49J20: Optimal control problems involving partial differential equations 49J40: Variational methods including variational inequalities
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 66 , Issue 2 , May 2023 , pp. 475 - 515
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

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