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Convergence Analysis of a New Bregman Extragradient Method for Solving Fixed Point Problems and Variational Inequality Problems in Reflexive Banach Spaces

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Abstract

We mainly introduce a new self-adaptive extragradient method by using the inertial technique for solving variational inequality problems of pseudomonotone operators and fixed point problems of Bregman relatively nonexpansive mappings in real reflexive Banach spaces. Precisely, we show that the sequence generated by our iterative process converges strongly to a common element for the solution set of variational inequality problems and the set of fixed points of Bregman relatively nonexpansive mappings. Additionally, some numerical examples are given to show the effectiveness of our algorithm. The results obtained in this paper are the improvement and supplement of many recent ones in the field.

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Funding

This work was supported by the NSF of China (Grant No. 12171435).

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Authors and Affiliations

  1. School of Marxism, Chongqing Normal University, Chongqing, Chongqing, 401331, China

    Shaotao Hu

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, 321004, China

    Shaotao Hu & Yuanheng Wang

  3. College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Qiao-Li Dong

Authors
  1. Shaotao Hu
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  2. Yuanheng Wang
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  3. Qiao-Li Dong
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The first draft of the manuscript was written by Shaotao Hu and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Yuanheng Wang.

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Hu, S., Wang, Y. & Dong, QL. Convergence Analysis of a New Bregman Extragradient Method for Solving Fixed Point Problems and Variational Inequality Problems in Reflexive Banach Spaces. J Sci Comput 96, 19 (2023). https://doi.org/10.1007/s10915-023-02243-0

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  • DOI: https://doi.org/10.1007/s10915-023-02243-0

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