Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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A TECHNIQUE WITH DIMINISHING AND NON-SUMMABLE STEP-SIZE FOR MONOTONE INCLUSION PROBLEMS IN BANACH SPACES

  • Abubakar Adamu (Operational Research Center in Healthcare, Near East University, Mathematics Institute, African University of Science and Technology) ;
  • Dilber Uzun Ozsahin (Department of Medical Diagnostic Imaging, College of Health Science, University of Sharjah, Research Institute for Medical and Health Sciences, University of Sharjah, Operational Research Center in Healthcare, Near East University) ;
  • Abdulkarim Hassan Ibrahim (Interdisciplinary Research Center for Smart Mobility and Logistics, King Fahd University of Petroleum and Minerals) ;
  • Pongsakorn Sunthrayuth (Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi)
  • Received : 2023.04.20
  • Accepted : 2023.07.18
  • Published : 2023.12.15
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Abstract

In this paper, an algorithm for approximating zeros of sum of three monotone operators is introduced and its convergence properties are studied in the setting of 2-uniformly convex and uniformly smooth Banach spaces. Unlike the existing algorithms whose step-sizes usually depend on the knowledge of the operator norm or Lipschitz constant, a nice feature of the proposed algorithm is the fact that it requires only a diminishing and non-summable step-size to obtain strong convergence of the iterates to a solution of the problem. Finally, the proposed algorithm is implemented in the setting of a classical Banach space to support the theory established.

Keywords

Acknowledgement

This research was supported by Thailand Science Research and Innovation Promotion Funding(TSRI)(Grant no.FRB660012/0168). This research block grants was managed under Rajamangala University of Technology Thanyaburi (FRB66E0628). The authors appreciate the supports of their institutions.

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