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An Iterative Algorithm to Approximate Fixed Points of Non-Linear Operators with an Application

Author

Listed:
  • Maryam Gharamah Alshehri

    (Computational & Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Faizan Ahmad Khan

    (Computational & Analytical Mathematics and Their Applications Research Group, Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia)

  • Faeem Ali

    (Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal 462003, India)

Abstract

In this article, we study the JF iterative algorithm to approximate the fixed points of a non-linear operator that satisfies condition (E) in uniformly convex Banach spaces. Further, some weak and strong convergence results are presented for the same operator using the JF iterative algorithm. We also demonstrate that the JF iterative algorithm is weakly w 2 G -stable with respect to almost contractions. In connection with our results, we provide some illustrative numerical examples to show that the JF iterative algorithm converges faster than some well-known iterative algorithms. Finally, we apply the JF iterative algorithm to estimate the solution of a functional non-linear integral equation. The results of the present manuscript generalize and extend the results in existing literature and will draw the attention of researchers.

Suggested Citation

  • Maryam Gharamah Alshehri & Faizan Ahmad Khan & Faeem Ali, 2022. "An Iterative Algorithm to Approximate Fixed Points of Non-Linear Operators with an Application," Mathematics, MDPI, vol. 10(7), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1132-:d:785230
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    References listed on IDEAS

    as
    1. Thakur, Balwant Singh & Thakur, Dipti & Postolache, Mihai, 2016. "A new iterative scheme for numerical reckoning fixed points of Suzuki’s generalized nonexpansive mappings," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 147-155.
    2. 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.
    3. Raul Argun & Alexandr Gorbachev & Dmitry Lukyanenko & Maxim Shishlenin, 2021. "On Some Features of the Numerical Solving of Coefficient Inverse Problems for an Equation of the Reaction-Diffusion-Advection-Type with Data on the Position of a Reaction Front," Mathematics, MDPI, vol. 9(22), pages 1-18, November.
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