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Convergence results of iterative algorithms for the sum of two monotone operators in reflexive Banach spaces

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Abstract

The aim of this paper is to propose two modified forward-backward splitting algorithms for zeros of the sum of a maximal monotone operator and a Bregman inverse strongly monotone operator in reflexive Banach spaces. We prove weak and strong convergence theorems of the generated sequences by the proposed methods under some suitable conditions. We apply our results to study the variational inequality problem and the equilibrium problem. Finally, a numerical example is given to illustrate the proposed methods. The results presented in this paper improve and generalize many known results in recent literature.

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Acknowledgements

The authors express their deep gratitude to the referee and the editor, their valuable comments and suggestions helped tremendously in improving the quality of this paper and made it suitable for publication.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, 400067, P. R. China

    Yan Tang

  2. Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathumthani, 12110, Thailand

    Ratthaprom Promkam

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

    Prasit Cholamjiak

  4. Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathumthani, 12110, Thailand

    Pongsakorn Sunthrayuth

Authors
  1. Yan Tang
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  2. Ratthaprom Promkam
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  3. Prasit Cholamjiak
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  4. Pongsakorn Sunthrayuth
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Correspondence to Pongsakorn Sunthrayuth.

Additional information

Y. Tang was funded by the Natural Science Foundation of Chongqing (CSTC2019JCYJmsxmX0661), the Science and Technology Research Project of Chongqing Municipal Education Commission (KJQN 201900804) and the Research Project of Chongqing Technology and Business University (KFJJ1952007). P. Cholamjiak was supported by Thailand Science Research and Innovation under the project IRN62W0007. P. Sunthrayuth was supported by the RMUTT Research Grant for New Scholar under Grant NSF62D0602.

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Tang, Y., Promkam, R., Cholamjiak, P. et al. Convergence results of iterative algorithms for the sum of two monotone operators in reflexive Banach spaces. Appl Math 67, 129–152 (2022). https://doi.org/10.21136/AM.2021.0108-20

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