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Three-Step Iterative Methodology for the Solution of Extended Ordered XOR-Inclusion Problems Incorporating Generalized Cayley–Yosida Operators

Author

Listed:
  • Doaa Filali

    (Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Imran Ali

    (Department of Mathematics, Koneru Lakshmaiah Education Foundation, Green Fields, Vaddeswaram 522302, Andhra Pradesh, India)

  • Montaser Saudi Ali

    (Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Nidal H. E. Eljaneid

    (Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Esmail Alshaban

    (Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Faizan Ahmad Khan

    (Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

Abstract

The system of extended ordered XOR-inclusion problems (in short, SEOXORIP) involving generalized Cayley and Yosida operators is introduced and studied in this paper. The solution is obtained in a real ordered Banach space using a fixed-point approach. First, we develop the fixed-point lemma for the solution of SEOXORIP. By using the fixed-point lemma, we develop a three-step iterative scheme for obtaining the approximate solution of SEOXORIP. Under the Lipschitz continuous assumptions of the cost mappings, the strong convergence of the scheme is demonstrated. Lastly, we provide a numerical example with a convergence graph generated using MATLAB 2018a to verify the convergence of the sequence generated by the proposed scheme.

Suggested Citation

  • Doaa Filali & Imran Ali & Montaser Saudi Ali & Nidal H. E. Eljaneid & Esmail Alshaban & Faizan Ahmad Khan, 2025. "Three-Step Iterative Methodology for the Solution of Extended Ordered XOR-Inclusion Problems Incorporating Generalized Cayley–Yosida Operators," Mathematics, MDPI, vol. 13(12), pages 1-24, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:1969-:d:1679140
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    References listed on IDEAS

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    1. Imran Ali & Rais Ahmad & Ching-Feng Wen, 2019. "Cayley Inclusion Problem Involving XOR-Operation," Mathematics, MDPI, vol. 7(3), pages 1-12, March.
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