A Novel Fixed-Point Iterative Process for Multivalued Mappings Applied in Solving a HIV Model of Fractional Order

Rubayyi T. Alqahtani (), Godwin Amechi Okeke and Cyril Ifeanyichukwu Ugwuogor
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Rubayyi T. Alqahtani: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh P.O. Box 90950, Saudi Arabia
Godwin Amechi Okeke: Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, Owerri P.M.B. 1526, Imo State, Nigeria
Cyril Ifeanyichukwu Ugwuogor: Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, Owerri P.M.B. 1526, Imo State, Nigeria

Mathematics, 2025, vol. 13, issue 5, 1-17

Abstract: We introduce a new and a faster iterative method for the approximation of the fixed point of multivalued nonexpansive mappings in the setting of uniformly convex Banach spaces. We prove some stability and data-dependence results for this novel iterative scheme. A series of numerical illustrations and examples was constructed to validate our results. As an application, we propose a novel method for solving a certain fractional differential equation using our newly developed iterative scheme. Our results extend, unify, and improve several of the known results in the literature.

Keywords: IA-iterative scheme; stability results; rate of convergence; data dependence; fixed-point iterative scheme; applications to HIV model of fractional order (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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