Novel Method for Approximating Fixed Point of Generalized α -Nonexpansive Mappings with Applications to Dynamics of a HIV Model

Godwin Amechi Okeke (), Akanimo Victor Udo and Rubayyi T. Alqahtani
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Godwin Amechi Okeke: Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, Owerri 460114, Nigeria
Akanimo Victor Udo: Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, Owerri 460114, Nigeria
Rubayyi T. Alqahtani: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi Arabia

Mathematics, 2025, vol. 13, issue 4, 1-26

Abstract: In this paper, we use an existing fixed point iterative scheme to approximate a class of generalized α -nonexpansive mapping in Banach spaces. We also prove weak and strong convergence results for the mapping using the AG iterative scheme. An example of a generalized α -nonexpansive mapping is given to show the validity of the claims. We apply the main results to the approximation of solution of a mixed type Voltera–Fredholm functional nonlinear integral equation and to the spread of HIV modeled in terms of a fractional differential equation of the Caputo type.

Keywords: AG iterative scheme; fixed point approximation; Caputo fractional differential equation; HIV model; Voltera–Fredholm functional nonlinear integral equation; generalized ?-nonexpansive mapping; modeling spread of HIV; fractional differential equation of Caputo type (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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