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Inertial method for a solution of Split Equality of Monotone Inclusion and the $f$-Fixed Point Problems in Banach Spaces
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  • Solomon Bekele Zegeye ,
  • Habtu Zegeye,
  • Mengstu Goa Sangago,
  • Oganeditse A. Boikanyo ,
  • Sebsibe T. Woldeamanuel
Solomon Bekele Zegeye
Addis Ababa University College of Natural Sciences

Corresponding Author:askubekele@gmail.com

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Habtu Zegeye
Botswana International University of Science and Technology
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Mengstu Goa Sangago
University of Botswana Faculty of Science
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Oganeditse A. Boikanyo
Botswana International University of Science and Technology
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Sebsibe T. Woldeamanuel
Kotebe Metropolitan University
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Abstract

In this paper, we propose an inertial algorithm for solving split equality of monotone inclusion and $f$-fixed point of Bregman relatively $f$-nonexpansive mapping problems in reflexive real Banach spaces. Using the Bregman distance function, we prove a strong convergence theorem for the algorithm produced by the method in real reflexive Banach spaces. As an application, we provide several applications of our method. Furthermore, we give a numerical example to demonstrate the behavior of the convergence of the algorithm.
19 Mar 2022Submitted to Mathematical Methods in the Applied Sciences
24 Mar 2022Submission Checks Completed
24 Mar 2022Assigned to Editor
25 Mar 2022Reviewer(s) Assigned
02 May 2022Review(s) Completed, Editorial Evaluation Pending
01 Jul 2022Editorial Decision: Revise Major
12 Jul 20221st Revision Received
13 Jul 2022Submission Checks Completed
13 Jul 2022Assigned to Editor
25 Jul 2022Reviewer(s) Assigned
07 Aug 2022Review(s) Completed, Editorial Evaluation Pending
11 Aug 2022Editorial Decision: Accept
27 Aug 2022Published in Mathematical Methods in the Applied Sciences. 10.1002/mma.8678