Semilocal Convergence of a Class of Modified Super-Halley Methods in Banach Spaces |
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| Authors: | Xiuhua Wang Jisheng Kou Chuanqing Gu |
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| Institution: | (1) School of Mathematics and Statistics, Xiaogan University, Xiaogan, 432100, Hubei, China;(2) Department of Mathematics, Shanghai University, Shanghai, 200444, China; |
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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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| Keywords: | |
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