IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v266y2015icp1031-1037.html
   My bibliography  Save this article

Ball convergence comparison between three iterative methods in Banach space under hypothese only on the first derivative

Author

Listed:
  • Argyros, Ioannis K.
  • George, Santhosh

Abstract

We present a convergence ball comparison between three iterative methods for approximating a locally unique solution of a nonlinear equation in a Banach space setting. The convergence ball and error estimates are given for these methods under hypotheses only on the first Fréchet derivative in contrast to earlier studies such as Adomian (1994) [1], Babajee et al. (2008) [13], Cordero and Torregrosa (2007) [17], Cordero et al. [18], Darvishi and Barati (2007) [19], using hypotheses reaching up to the fourth Fréchet derivative although only the first derivative appears in these methods. This way we expand the applicability of these methods. Numerical examples are also presented in this study.

Suggested Citation

  • Argyros, Ioannis K. & George, Santhosh, 2015. "Ball convergence comparison between three iterative methods in Banach space under hypothese only on the first derivative," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 1031-1037.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:1031-1037
    DOI: 10.1016/j.amc.2015.06.031
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315008127
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.06.031?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. M. A. Hernández, 2000. "Second-Derivative-Free Variant of the Chebyshev Method for Nonlinear Equations," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 501-515, March.
    2. Sharma, Janak Raj, 2015. "Improved Chebyshev–Halley methods with sixth and eighth order convergence," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 119-124.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ramandeep Behl & Eulalia Martínez & Fabricio Cevallos & Diego Alarcón, 2019. "A Higher Order Chebyshev-Halley-Type Family of Iterative Methods for Multiple Roots," Mathematics, MDPI, vol. 7(4), pages 1-12, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:1031-1037. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.