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Approximation of Fixed Points for Suzuki’s Generalized Non-Expansive Mappings

Author

Listed:
  • Javid Ali

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India)

  • Faeem Ali

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India)

  • Puneet Kumar

    (Department of Mathematics and Statistics, Fiji National University, P.O. Box 3722, Samabula, Fiji)

Abstract

In this paper, we study a three step iterative scheme to approximate fixed points of Suzuki’s generalized non-expansive mappings. We establish some weak and strong convergence results for such mappings in uniformly convex Banach spaces. Further, we show numerically that the considered iterative scheme converges faster than some other known iterations for Suzuki’s generalized non-expansive mappings. To support our claim, we give an illustrative numerical example and approximate fixed points of such mappings using Matlab program. Our results are new and generalize several relevant results in the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:522-:d:237869
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    References listed on IDEAS

    as
    1. B. E. Rhoades, 1991. "Some fixed point iteration procedures," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 14, pages 1-16, January.
    2. Wissam Kassab & Teodor Ţurcanu, 2019. "Numerical Reckoning Fixed Points of ( ρE )-Type Mappings in Modular Vector Spaces," Mathematics, MDPI, vol. 7(5), pages 1-13, April.
    3. M. De la Sen & Mujahid Abbas, 2019. "On Best Proximity Results for a Generalized Modified Ishikawa’s Iterative Scheme Driven by Perturbed 2-Cyclic Like-Contractive Self-Maps in Uniformly Convex Banach Spaces," Journal of Mathematics, Hindawi, vol. 2019, pages 1-15, January.
    4. 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.
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    Cited by:

    1. 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.
    2. Konrawut Khammahawong & Parin Chaipunya & Kamonrat Sombut, 2022. "Approximating Common Fixed Points of Nonexpansive Mappings on Hadamard Manifolds with Applications," Mathematics, MDPI, vol. 10(21), pages 1-20, November.
    3. 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.

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