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Semilocal Convergence of a Class of Modified Super-Halley Methods in Banach Spaces

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Abstract

In this paper, we consider the semilocal convergence of a class of modified super-Halley methods for solving nonlinear equations in Banach spaces. The semilocal convergence of this class of methods is established by using recurrence relations. We construct a system of recurrence relations for the methods, and based on it, we prove an existence–uniqueness theorem that shows the R-order of the methods.

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Acknowledgements

This work is supported by the Scientific and Technical Research Project of Hubei Provincial Department of Education (Q20112702), by Shanghai Leading Academic Discipline Project (J50101) and by Key Disciplines of Shanghai Municipality (S30104).

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Correspondence to Jisheng Kou.

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Communicated by Ilio Galligani.

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Wang, X., Kou, J. & Gu, C. Semilocal Convergence of a Class of Modified Super-Halley Methods in Banach Spaces. J Optim Theory Appl 153, 779–793 (2012). https://doi.org/10.1007/s10957-012-9985-9

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  • DOI: https://doi.org/10.1007/s10957-012-9985-9

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