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A Cyclic Iterative Algorithm for Multiple-Sets Split Common Fixed Point Problem of Demicontractive Mappings without Prior Knowledge of Operator Norm

Author

Listed:
  • Nishu Gupta

    (Department of Mathematics, Pt NRS Government College, Rohtak 124001, India
    These authors contributed equally to this work.)

  • Mihai Postolache

    (Department of General Education, China Medical University, Taichung 40402, Taiwan
    Department of Interior Design, Asia University, Taichung 41354, Taiwan
    Gh. Mihoc-C. Iacob Institute of Mathematical Statistics and Applied Mathematics, Romanian Academy, 050711 Bucharest, Romania
    Department of Mathematics and Informatics, University “Politehnica” of Bucharest, 060042 Bucharest, Romania)

  • Ashish Nandal

    (Government College, Bhainswal Kalan 131001, India
    These authors contributed equally to this work.)

  • Renu Chugh

    (Department of Mathematics, Maharshi Dayanand University, Rohtak 124001, India
    These authors contributed equally to this work.)

Abstract

The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:4:p:372-:d:498667
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    References listed on IDEAS

    as
    1. Boikanyo, Oganeditse A., 2015. "A strongly convergent algorithm for the split common fixed point problem," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 844-853.
    2. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
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    Cited by:

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    2. 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.

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