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Iterative methods with perturbations for the sum of two accretive operators in q-uniformly smooth Banach spaces

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this work, we introduce implicit and explicit iteration processes with perturbations for solving the fixed point problem of nonexpansive mappings and the quasi-variational inclusion problem. We then prove its strong convergence under some suitable conditions. In the last section of the paper, some applications are given also. The results obtained in this paper extend and improve some known others presented in the literature.

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Acknowledgements

S. Suantai would like to thank Chiang Mai University for financial supports, P. Cholamjiak was supported by the Thailand Research Fund and the Commission on Higher Education under Grant MRG5980248 and P. Sunthrayuth was supported by RMUTT research foundation scholarship of Rajamangala University of Technology Thanyaburi under Grant NRF04066005.

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Authors and Affiliations

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

    Suthep Suantai

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

    Prasit Cholamjiak

  3. 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

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  1. Suthep Suantai
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  2. Prasit Cholamjiak
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  3. Pongsakorn Sunthrayuth
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Correspondence to Pongsakorn Sunthrayuth.

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Suantai, S., Cholamjiak, P. & Sunthrayuth, P. Iterative methods with perturbations for the sum of two accretive operators in q-uniformly smooth Banach spaces. RACSAM 113, 203–223 (2019). https://doi.org/10.1007/s13398-017-0465-9

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  • DOI: https://doi.org/10.1007/s13398-017-0465-9

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