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Shrinking projection methods involving inertial forward–backward splitting methods for inclusion problems

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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 paper, we propose a modified forward–backward splitting method using the shrinking projection and the inertial technique for solving the inclusion problem of the sum of two monotone operators. We prove its strong convergence under some suitable conditions in Hilbert spaces. We provide some numerical experiments including a comparison to show the implementation and the efficiency of our method.

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Acknowledgements

S.A. Khan would like to thank BITS-Pilani, Dubai Campus. S. Suantai was supported by Chiang Mai University. W. Cholamjiak would like to thank the Thailand Research Fund under the Project MRG6080105 and University of Phayao.

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Authors and Affiliations

  1. Department of Mathematics, BITS-Pilani, Dubai Campus, P.O. Box 345055, Dubai, UAE

    Suhel Ahmad Khan

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

    Suthep Suantai

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

    Watcharaporn Cholamjiak

Authors
  1. Suhel Ahmad Khan
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  2. Suthep Suantai
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  3. Watcharaporn Cholamjiak
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Correspondence to Watcharaporn Cholamjiak.

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Khan, S.A., Suantai, S. & Cholamjiak, W. Shrinking projection methods involving inertial forward–backward splitting methods for inclusion problems. RACSAM 113, 645–656 (2019). https://doi.org/10.1007/s13398-018-0504-1

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  • DOI: https://doi.org/10.1007/s13398-018-0504-1

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