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

Doaa Filali, Imran Ali (), Montaser Saudi Ali, Nidal H. E. Eljaneid, Esmail Alshaban and Faizan Ahmad Khan ()
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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

Mathematics, 2025, vol. 13, issue 12, 1-24

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.

Keywords: ordered inclusions; Cayley–Yosida Operators; three-step iterative scheme; strong convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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