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Iterative methods for solving quasi-variational inclusion and fixed point problem in q-uniformly smooth Banach spaces

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Abstract

In this work, we introduce implicit and explicit iterations for solving the variational inclusion problem for the sum of two operators and the fixed point problem of nonexpansive mappings. We then prove its strong convergence theorems in the framework of Banach spaces. We finally provide some applications of the main results.

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Acknowledgments

The authors would like to thank editor and reviewers for valuable comments. P. Sunthrayuth was supported by RMUTT research foundation scholarship of the Rajamangala University of Technology Thanyaburi (Grant No. NRF04066005). P. Cholamjiak was supported by the Thailand Research Fund and the Commission on Higher Education under Grant MRG5980248.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), 39 Rangsit-Nakhonnayok Rd., Klong 6, Thanyaburi, Pathumthani, 12110, Thailand

    Pongsakorn Sunthrayuth

  2. School of Science, University of Phayao, Phayao, 56000, Thailand

    Prasit Cholamjiak

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  1. Pongsakorn Sunthrayuth
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  2. Prasit Cholamjiak
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Correspondence to Prasit Cholamjiak.

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Sunthrayuth, P., Cholamjiak, P. Iterative methods for solving quasi-variational inclusion and fixed point problem in q-uniformly smooth Banach spaces. Numer Algor 78, 1019–1044 (2018). https://doi.org/10.1007/s11075-017-0411-0

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  • DOI: https://doi.org/10.1007/s11075-017-0411-0

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