## 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.

Original language | English |
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Pages (from-to) | 475-515 |

Number of pages | 41 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 66 |

Issue number | 2 |

DOIs | |

Publication status | Published - 15 May 2023 |

Externally published | Yes |

### Bibliographical note

Funding Information:The second author is supported by the National Research Foundation of South Africa Incentive Funding for Rated Researchers (grant number 119903). The third author is funded by University of KwaZulu-Natal, Durban, South Africa, Postdoctoral Fellowship. He is grateful for the funding and financial support.

Publisher Copyright:

© The Author(s), 2023. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

## Keywords

- Banach spaces
- Bregman distance
- equilibrium problem
- fixed-point problem
- p-uniformly convex
- pseudomonotone bifunction
- quasi-nonexpansive mapping
- split feasibility problem
- strong convergence

## ASJC Scopus subject areas

- General Mathematics