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Convergence Theorem for a Family of New Modified Halley’s Method in Banach Space

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Listed:
  • Rongfei Lin
  • Yueqing Zhao
  • Qingbiao Wu
  • Jueliang Hu

Abstract

We establish convergence theorems of Newton‐Kantorovich type for a family of new modified Halley’s method in Banach space to solve nonlinear operator equations. We present the corresponding error estimate. To show the application of our theorems, two numerical examples are given.

Suggested Citation

  • Rongfei Lin & Yueqing Zhao & Qingbiao Wu & Jueliang Hu, 2014. "Convergence Theorem for a Family of New Modified Halley’s Method in Banach Space," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:468694
    DOI: 10.1155/2014/468694
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    References listed on IDEAS

    as
    1. Rongfei Lin & Yueqing Zhao & Zdeněk Šmarda & Yasir Khan & Qingbiao Wu, 2013. "Newton-Kantorovich and Smale Uniform Type Convergence Theorem for a Deformed Newton Method in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, December.
    2. Rongfei Lin & Yueqing Zhao & Zdeněk Šmarda & Yasir Khan & Qingbiao Wu, 2013. "Newton‐Kantorovich and Smale Uniform Type Convergence Theorem for a Deformed Newton Method in Banach Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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