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

Author

Listed:
  • 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
    These authors contributed equally to this work.)

  • 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
    These authors contributed equally to this work.)

  • Rubayyi T. Alqahtani

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11623, Saudi Arabia
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Godwin Amechi Okeke & Akanimo Victor Udo & Rubayyi T. Alqahtani, 2025. "Novel Method for Approximating Fixed Point of Generalized α -Nonexpansive Mappings with Applications to Dynamics of a HIV Model," Mathematics, MDPI, vol. 13(4), pages 1-26, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:4:p:550-:d:1586072
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