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Self-adaptive algorithms for solving split feasibility problem with multiple output sets

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Abstract

In this paper, we study the split feasibility problem with multiple output sets in Hilbert spaces. For solving the aforementioned problem, we propose two new self-adaptive relaxed CQ algorithms which involve computing of projections onto half-spaces instead of computing onto the closed convex sets, and it does not require calculating the operator norm. We establish a weak and a strong convergence theorems for the proposed algorithms. We apply the new results to solve some other problems. Finally, we present some numerical examples to show the efficiency and accuracy of our algorithm compared to some existing results. Our results extend and improve some existing methods in the literature.

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Acknowledgements

The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Guash Haile Taddele is supported by the Petchra Pra Jom Klao Ph.D. Research Scholarship from King Mongkut’s University of Technology Thonburi (Grant No.37/2561). Moreover, we would like to thank the Editor and Reviewers for taking the time and effort necessary to review the manuscript. We sincerely appreciate all valuable comments and suggestions, which helped us to improve the quality of the manuscript.

The authors acknowledge the financial support provided by “Mid-Career Research Grant” (N41A640089).

Funding

This research was funded by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, KMUTT. The first author was supported by the Petchra Pra Jom Klao Ph.D. Research Scholarship from King Mongkut’s University of Technology Thonburi with Grant No. 37/2561.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Guash Haile Taddele

  2. Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 26 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Poom Kumam

  3. Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Thanyaburi, Pathumthani, 12110, Thailand

    Pongsakorn Sunthrayuth

  4. Department of Mathematics, College of Computational and Natural Science, Debre Berhan University, Debre Berhan, PO. Box 445, Ethiopia

    Anteneh Getachew Gebrie

  5. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan

    Poom Kumam

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  1. Guash Haile Taddele
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  4. Anteneh Getachew Gebrie
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Correspondence to Poom Kumam.

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Taddele, G.H., Kumam, P., Sunthrayuth, P. et al. Self-adaptive algorithms for solving split feasibility problem with multiple output sets. Numer Algor 92, 1335–1366 (2023). https://doi.org/10.1007/s11075-022-01343-6

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