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A parallel monotone hybrid algorithm for a finite family of \(G-\)nonexpansive mappings in Hilbert spaces endowed with a graph applicable in signal recovery

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Abstract

In this paper, we modified the shrinking projection method with the parallel monotone hybrid method for approximating common fixed points of a finite family of G-nonexpansive mappings. We then prove a strong convergence theorem under suitable conditions in Hilbert spaces endowed with graphs. Moreover, we give some numerical examples and compare the rate of convergence of our algorithms. Finally, we provide an application to signal recovery in a situation without knowing the type of noises and demonstrate the computational performance of our algorithm in comparison to some methods. The numerical results of the comparative analysis are also discussed.

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Acknowledgements

S. Suantai would like to thank Chiang Mai University, K. Kankam would like to thank Thailand Science Research and Innovation under the project IRN62W0007 and W. Cholamjiak would like to thank the revenue budget in 2021, School of Science, University of Phayao.

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Authors and Affiliations

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

    Suthep Suantai

  2. Data Science Research Center, 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

    Kunrada Kankam, Prasit Cholamjiak & Watcharaporn Cholamjiak

Authors
  1. Suthep Suantai
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  2. Kunrada Kankam
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  3. Prasit Cholamjiak
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  4. Watcharaporn Cholamjiak
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Corresponding author

Correspondence to Watcharaporn Cholamjiak.

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Communicated by Carlos Hoppen.

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Suantai, S., Kankam, K., Cholamjiak, P. et al. A parallel monotone hybrid algorithm for a finite family of \(G-\)nonexpansive mappings in Hilbert spaces endowed with a graph applicable in signal recovery. Comp. Appl. Math. 40, 145 (2021). https://doi.org/10.1007/s40314-021-01530-6

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  • DOI: https://doi.org/10.1007/s40314-021-01530-6

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