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Split Null Point Problems and Fixed Point Problems for Demicontractive Multivalued Mappings

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Abstract

In this paper, we consider the split null point problem and the fixed point problem for multivalued mappings in Hilbert spaces. We introduce a Halpern-type algorithm for solving the problem for maximal monotone operators and demicontractive multivalued mappings, and establish a strong convergence result under some suitable conditions. Also, we apply our problem of main result to other split problems, that is, the split feasibility problem, the split equilibrium problem, and the split minimization problem. Finally, a numerical result for supporting our main result is also supplied.

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Acknowledgements

The authors would like to thank the referees for valuable comments and suggestions for improving this work and Chiang Mai University for the financial support.

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Authors and Affiliations

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

    Pachara Jailoka

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

    Suthep Suantai

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

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Jailoka, P., Suantai, S. Split Null Point Problems and Fixed Point Problems for Demicontractive Multivalued Mappings. Mediterr. J. Math. 15, 204 (2018). https://doi.org/10.1007/s00009-018-1251-4

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  • DOI: https://doi.org/10.1007/s00009-018-1251-4

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