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

• Published in: Mathematics (Basel) Vol. 13; no. 4; p. 550
• Main Authors: Okeke, Godwin Amechi, Udo, Akanimo Victor, Alqahtani, Rubayyi T
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.02.2025
• Subjects: Acquired immune deficiency syndrome; AG iterative scheme; AIDS; Applied mathematics; Approximation; Banach spaces; Boundary value problems; Caputo fractional differential equation; Differential equations; fixed point approximation; Fractional calculus; generalized α-nonexpansive mapping; HIV; HIV (Viruses); HIV model; Human immunodeficiency virus; Integral equations; Mapping; Methods; Ordinary differential equations; Partial differential equations; Voltera–Fredholm functional nonlinear integral equation
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math13040550

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.