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Algorithms for finding a common element of the set of common fixed points for nonexpansive semigroups, variational inclusions and generalized equilibrium 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 work, we introduced an iterative algorithm for finding a common element of the set of common fixed points of a one-parameter nonexpansive semigroup, the set of solutions to a variational inclusion and the set of solutions to a generalized equilibrium problem in a real Hilbert space. Furthermore, we proved the convergence theorem of the proposed iterative algorithm under some mild conditions on algorithm parameters. Finally, we gave some numerical examples which support our main theorem at last part. The results presented in this paper generalize the well-known theorems.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China ( 11771347, 91730306, 41390454).

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, People’s Republic of China

    Meng Wen & Jigen Peng

  2. School of Science, Xi’an Polytechnic University, Xi’an, 710048, People’s Republic of China

    Meng Wen

  3. Department of Mathematics, Hubei Normal University, Huangshi, 435002, People’s Republic of China

    Changsong Hu

  4. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Angang Cui

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  1. Meng Wen
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  2. Changsong Hu
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  3. Angang Cui
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  4. Jigen Peng
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Correspondence to Meng Wen or Jigen Peng.

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Wen, M., Hu, C., Cui, A. et al. Algorithms for finding a common element of the set of common fixed points for nonexpansive semigroups, variational inclusions and generalized equilibrium problems. RACSAM 114, 175 (2020). https://doi.org/10.1007/s13398-020-00906-3

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  • DOI: https://doi.org/10.1007/s13398-020-00906-3

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