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Semilocal convergence for a family of Chebyshev-Halley like iterations under a mild differentiability condition

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Abstract

The semilocal convergence of a family of Chebyshev-Halley like iterations for nonlinear operator equations is studied under the hypothesis that the first derivative satisfies a mild differentiability condition. This condition includes the usual Lipschitz condition and the Hölder condition as special cases. The method employed in the present paper is based on a family of recurrence relations. The R-order of convergence of the methods is also analyzed. As well, an application to a nonlinear Hammerstein integral equation of the second kind is provided. Furthermore, two numerical examples are presented to demonstrate the applicability and efficiency of the convergence results.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Xiubin Xu & Yonghui Ling

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  1. Xiubin Xu
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  2. Yonghui Ling
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Correspondence to Xiubin Xu.

Additional information

Supported in part by the National Natural Science Foundation of China (Grants No. 61170109 and No. 10971194) and Zhejiang Innovation Project (Grant No. T200905).

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Xu, X., Ling, Y. Semilocal convergence for a family of Chebyshev-Halley like iterations under a mild differentiability condition. J. Appl. Math. Comput. 40, 627–647 (2012). https://doi.org/10.1007/s12190-012-0557-9

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  • DOI: https://doi.org/10.1007/s12190-012-0557-9

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