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A Self-Adaptive Algorithm for Split Null Point Problems and Fixed Point Problems for Demicontractive Multivalued Mappings

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Abstract

In this work, we study the split null point problem and the fixed point problem in Hilbert spaces. We introduce a self-adaptive algorithm based on the viscosity approximation method without prior knowledge of the operator norm for finding a common solution of the considered problem for maximal monotone mappings and demicontractive multivalued mappings. A strong convergence result of our proposed algorithm is established under some suitable conditions. Some convergence results for the split feasibility problem and the split minimization problem are consequences of our main result. Finally, we also give numerical examples for supporting our main result.

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Acknowledgements

The authors would like to thank the referees for valuable comments and suggestions for improving this work. P. Jailoka was supported by Post-Doctoral Fellowship of Chiang Mai University, Thailand. We also would like to thank Chiang Mai University for the financial support.

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Authors and Affiliations

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

    Suthep Suantai & Pachara Jailoka

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  1. Suthep Suantai
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  2. Pachara Jailoka
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Correspondence to Pachara Jailoka.

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Suantai, S., Jailoka, P. A Self-Adaptive Algorithm for Split Null Point Problems and Fixed Point Problems for Demicontractive Multivalued Mappings. Acta Appl Math 170, 883–901 (2020). https://doi.org/10.1007/s10440-020-00362-6

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  • DOI: https://doi.org/10.1007/s10440-020-00362-6

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