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A New CQ Algorithm for Solving Split Feasibility Problems in Hilbert Spaces

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Abstract

In this paper, we propose a CQ-type algorithm for solving the split feasibility problem (SFP) in real Hilbert spaces. The algorithm is designed such that the step-sizes are directly computed at each iteration. We will show that the sequence generated by the proposed algorithm converges in norm to the minimum-norm solution of the SFP under appropriate conditions. In addition, we give some numerical examples to verify the implementation of our method. Our result improves and complements many known related results in the literature.

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Acknowledgements

P. Cholamjiak was supported by the Thailand Research Fund and the Commission on Higher Education under Grant MRG5980248. S. Suantai was partially supported by Chiang Mai University.

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Authors and Affiliations

  1. Applied Analysis Research Group, Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Nguyen The Vinh

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

    Prasit Cholamjiak

  3. Center of Excellence in Mathematics and Applied Mathematics, Department of Mathematics, Chiang Mai University, Chiang Mai, 50200, Thailand

    Suthep Suantai

Authors
  1. Nguyen The Vinh
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  2. Prasit Cholamjiak
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  3. Suthep Suantai
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Correspondence to Prasit Cholamjiak.

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Mohammad Sal Moslehian.

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Vinh, N.T., Cholamjiak, P. & Suantai, S. A New CQ Algorithm for Solving Split Feasibility Problems in Hilbert Spaces. Bull. Malays. Math. Sci. Soc. 42, 2517–2534 (2019). https://doi.org/10.1007/s40840-018-0614-0

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  • DOI: https://doi.org/10.1007/s40840-018-0614-0

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