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Semilocal convergence for a class of improved multi-step Chebyshev–Halley-like methods under extended conditions

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Abstract

Semilocal convergence for a class of improved multi-step Chebyshev–Halley-like methods is considered in this paper. Compared with the results for the Chebyshev method in Hernández (J Comput Appl Math 126:131–143, 2000), the R-order of convergence is heightened and the Hölder continuity of second derivative is also relaxed. Moreover, an existence-uniqueness theorem is proved under the extended conditions.

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

    Xiuhua Wang & Jisheng Kou

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  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 for a class of improved multi-step Chebyshev–Halley-like methods under extended conditions. J. Fixed Point Theory Appl. 20, 122 (2018). https://doi.org/10.1007/s11784-018-0599-1

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  • DOI: https://doi.org/10.1007/s11784-018-0599-1

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