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Algorithms for Approximating Solutions of Split Variational Inclusion and Fixed-Point Problems

Author

Listed:
  • Li-Jun Zhu

    (The Key Laboratory of Intelligent Information and Big Data Processing of Ningxia, North Minzu University, Yinchuan 750021, China)

  • Yonghong Yao

    (School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
    Center for Advanced Information Technology, Kyung Hee University, Seoul 02447, Republic of Korea)

Abstract

In this paper, the split fixed point and variational inclusion problem is considered. With the help of fixed point technique, Tseng-type splitting method and self-adaptive rule, an iterative algorithm is proposed for solving this split problem in which the involved operators S and T are demicontractive operators and g is plain monotone. Strong convergence theorem is proved under some mild conditions.

Suggested Citation

  • Li-Jun Zhu & Yonghong Yao, 2023. "Algorithms for Approximating Solutions of Split Variational Inclusion and Fixed-Point Problems," Mathematics, MDPI, vol. 11(3), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:641-:d:1047988
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    References listed on IDEAS

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    1. Nishu Gupta & Mihai Postolache & Ashish Nandal & Renu Chugh, 2021. "A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm," Mathematics, MDPI, vol. 9(4), pages 1-19, February.
    2. Cristina Ticala & Ioana Zelina & Camelia-M. Pintea, 2020. "Admissible Perturbation of Demicontractive Operators within Ant Algorithms for Medical Images Edge Detection," Mathematics, MDPI, vol. 8(6), pages 1-13, June.
    3. Peeyada, Pronpat & Suparatulatorn, Raweerote & Cholamjiak, Watcharaporn, 2022. "An inertial Mann forward-backward splitting algorithm of variational inclusion problems and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
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    Cited by:

    1. Kasamsuk Ungchittrakool & Somyot Plubtieng & Natthaphon Artsawang & Purit Thammasiri, 2023. "Modified Mann-Type Algorithm for Two Countable Families of Nonexpansive Mappings and Application to Monotone Inclusion and Image Restoration Problems," Mathematics, MDPI, vol. 11(13), pages 1-21, June.
    2. Ahmed Alamer & Mohammad Dilshad, 2024. "Halpern-Type Inertial Iteration Methods with Self-Adaptive Step Size for Split Common Null Point Problem," Mathematics, MDPI, vol. 12(5), pages 1-16, March.

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