DOI: 10.24193/fpt-ro.2022.1.01

Authors: H.A. Abass, A.A. Mebawondu, C. Izuchukwu and O.K. Narain

Abstract: In this paper, we study split common fixed point problems of Bregman demigeneralized and Bregman quasi-nonexpansive mappings in reflexive Banach spaces. Using the Bregman technique together with a Halpern iterative algorithm, we approximate a solution of split common fixed point problem and sum of two monotone operators in reflexive Banach spaces. We establish a strong convergence result for approximating the solution of the aforementioned problems. It is worth mentioning that the iterative algorithm employ in this article is design in such a way that it does not require prior knowledge of operator norm and we do not employ Fejer monotinicity condition in the strategy of proving our convergence theorem. We apply our result to solve variational inequality and convex minimization problems. The result discuss in this paper extends and complements many related results in literature.

Key Words and Phrases: Bregman quasi-nonexpansive, Bregman demigeneralized mapping, monotone operators, fixed point, iterative scheme, split common fixed point problem.

2010 Mathematics Subject Classification: 47H06, 47H09, 47J05, 47J25, 47H10.

Published on-line: February 1st, 2022.

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