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Hybrid inertial accelerated algorithms for split fixed point problems of demicontractive mappings and equilibrium problems

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Abstract

Our contribution in this paper, we introduce and analyze two new hybrid algorithms by combining Mann iteration and inertial method for solving split fixed point problems of demicontractive mappings and equilibrium problems in a real Hilbert space. By using a new technique of choosing step size, our algorithms do not need any prior information on the operator norm. In fact, an inertial type algorithm was proposed in order to accelerate its convergence rate. We then prove weak and strong convergence of proposed methods under some control conditions. Moreover, some numerical experiments for image restoration problems and oligopolistic market equilibrium problems are also provided for supporting our main results.

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Funding

This study was financially supported by Chiang Mai University.

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Authors and Affiliations

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

    Adisak Hanjing

  2. Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand

    Suthep Suantai

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  1. Adisak Hanjing
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  2. Suthep Suantai
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Correspondence to Suthep Suantai.

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Hanjing, A., Suantai, S. Hybrid inertial accelerated algorithms for split fixed point problems of demicontractive mappings and equilibrium problems. Numer Algor 85, 1051–1073 (2020). https://doi.org/10.1007/s11075-019-00855-y

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  • DOI: https://doi.org/10.1007/s11075-019-00855-y

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