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

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.