Hybrid extragradient-type algorithm for zeros and fixed point problems in Banach spaces

Subject Areas : Fixed point theory

B. Ali ¹ , A. A. Alasan ²

1 - Department of Mathematical Sciences, Bayero University, Kano, Nigeria
2 - Department of Mathematical Sciences, Bayero University, Kano, Nigeria; Department of Basic Studies, Kano State Polytechnic, Kano, Nigeria

Received: 2023-10-18 Accepted : 2024-01-30 Published : 2024-02-14

Keywords: equilibrium problem, maximal monotone operator, Bregman inverse strongly monotone operator, Bregman demigeneralized mapping,

Abstract :

In this paper, we introduce a new hybrid extragradient-type algorithm for approximating an element in the set of common solutions of equilibrium problems and common fixed points of family of Bregman demigeneralized mappings which is also a common zero of the sum of maximal monotone and Bregman inverse strongly monotone operators in the setting of reflexie Banach space. Strong convergence of the proposed algorithm to a solutions of the said problems is established which improves and generalizes many recently announced results in the literature.

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