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Convergence of AA-Iterative Algorithm for Generalized α -Nonexpansive Mappings with an Application

Author

Listed:
  • Ismat Beg

    (Department of Mathematics and Statistical Sciences, Lahore School of Economics, Lahore 53200, Pakistan)

  • Mujahid Abbas

    (Department of Mathematics, Government College University, Lahore 54000, Pakistan
    Department of Medical Research, China Medical University, Taichung 40402, Taiwan)

  • Muhammad Waseem Asghar

    (Department of Mathematics, Government College University, Lahore 54000, Pakistan)

Abstract

The aim of this paper is to approximate the fixed points of generalized α -nonexpansive mappings using A A -iterative algorithm. We establish some weak and strong convergence results for generalized α -nonexpansive mappings in uniformly convex Banach spaces. A numerical example is also given to show that the A A -iterative algorithm converges faster than some others algorithms for generalized α -nonexpansive mappings. Lastly, using the A A -iterative algorithm, we approximate the weak solution of delay composite functional differential equation of the Volterra–Stieltjes type.

Suggested Citation

  • Ismat Beg & Mujahid Abbas & Muhammad Waseem Asghar, 2022. "Convergence of AA-Iterative Algorithm for Generalized α -Nonexpansive Mappings with an Application," Mathematics, MDPI, vol. 10(22), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4375-:d:978696
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    References listed on IDEAS

    as
    1. Javid Ali & Faeem Ali & Puneet Kumar, 2019. "Approximation of Fixed Points for Suzuki’s Generalized Non-Expansive Mappings," Mathematics, MDPI, vol. 7(6), pages 1-11, June.
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