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Semilocal convergence of multi-point improved super-Halley-type methods without the second derivative under generalized weak condition

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Abstract

In this paper, we consider the semilocal convergence of multi-point improved super-Halley-type methods in Banach space. Different from the results of super-Halley method studied in reference Gutiérrez, J.M. and Hernández, M.A. (Comput. Math. Appl. 36,1–8, 1998) these methods do not require second derivative of an operator, the R-order is improved and the convergence condition is also relaxed. We prove a convergence theorem to show existence and uniqueness of the solution.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hubei Engineering University, Xiaogan, 432000, Hubei, China

    Xiuhua Wang & Jisheng Kou

  2. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, 450052, China

    Xiuhua Wang

Authors
  1. Xiuhua Wang
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  2. Jisheng Kou
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Correspondence to Jisheng Kou.

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Wang, X., Kou, J. Semilocal convergence of multi-point improved super-Halley-type methods without the second derivative under generalized weak condition. Numer Algor 71, 567–584 (2016). https://doi.org/10.1007/s11075-015-0010-x

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  • DOI: https://doi.org/10.1007/s11075-015-0010-x

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