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On Split Fixed Point Problems for Multi-Valued Mappings and Designing a Self-Adaptive Method

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Abstract

Over the past decades, the split inverse problem has been widely studied, and one of the objectives of those researches is to invent some efficient algorithms for approximating solutions. Most of those algorithms depend on the norms of bounded linear operators; however, the calculation of the operator norms is not an easy task in general practice. In this article, we study and investigate the split fixed point problem for multi-valued mappings in Hilbert spaces. We introduce a self-adaptive algorithm without prior knowledge of the operator norm for two demicontractive multi-valued mappings, and establish a strong convergence theorem of the proposed method under some suitable conditions. Our main result in this paper generalizes and improves many results in the literature.

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Acknowledgements

The authors are thankful to the anonymous referee for valuable comments and suggestions to improve the quality of the paper. S. Suantai would like to thank Chiang Mai University for the financial support.

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Authors and Affiliations

  1. Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand

    Pachara Jailoka & Suthep Suantai

  2. Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand

    Pachara Jailoka & Suthep Suantai

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  1. Pachara Jailoka
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  2. Suthep Suantai
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Jailoka, P., Suantai, S. On Split Fixed Point Problems for Multi-Valued Mappings and Designing a Self-Adaptive Method. Results Math 76, 133 (2021). https://doi.org/10.1007/s00025-021-01441-2

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