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On the Convergence of the Yosida–Cayley Variational Inclusion Problem with the XOR Operation and Inertial Extrapolation Scheme

Author

Listed:
  • Arifuzzaman

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, UP, India)

  • Syed Shakaib Irfan

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, UP, India)

  • Iqbal Ahmad

    (Department of Mechanical Engineering, College of Engineering, Qassim University, Saudi Arabia)

Abstract

This article studies the structure and properties of real-ordered Hilbert spaces, highlighting the roles of the XOR and XNOR logical operators in conjunction with the Yosida and Cayley approximation operators. These fundamental elements are utilized to formulate the Yosida–Cayley Variational Inclusion Problem (YCVIP) and its associated Yosida–Cayley Resolvent Equation Problem (YCREP). To address these problems, we develop and examine several solution methods, with particular attention given to the convergence behavior of the proposed algorithms. We prove both the existence of solutions and the strong convergence of iterative sequences generated under the influence of the aforesaid operators. The theoretical results are supported by a numerical result, demonstrating the practical applicability and efficiency of the suggested approaches.

Suggested Citation

  • Arifuzzaman & Syed Shakaib Irfan & Iqbal Ahmad, 2025. "On the Convergence of the Yosida–Cayley Variational Inclusion Problem with the XOR Operation and Inertial Extrapolation Scheme," Mathematics, MDPI, vol. 13(15), pages 1-29, July.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:15:p:2447-:d:1712901
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    References listed on IDEAS

    as
    1. Imran Ali & Rais Ahmad & Ching-Feng Wen, 2019. "Cayley Inclusion Problem Involving XOR-Operation," Mathematics, MDPI, vol. 7(3), pages 1-12, March.
    2. Arvind Kumar Rajpoot & Mohd Ishtyak & Rais Ahmad & Yuanheng Wang & Jen-Chih Yao, 2023. "Convergence Analysis for Yosida Variational Inclusion Problem with Its Corresponding Yosida Resolvent Equation Problem through Inertial Extrapolation Scheme," Mathematics, MDPI, vol. 11(3), pages 1-19, February.
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