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• W2955740789 abstract "In this paper, we present a local convergence analysis of some iterative methods to approximate a locally unique solution of nonlinear equations in a Banach space setting. In the earlier study [Babajee et al. (2015) “On some improved harmonic mean Newton-like methods for solving systems of nonlinear equations,” Algorithms 8(4), 895–909], demonstrate convergence of their methods under hypotheses on the fourth-order derivative or even higher. However, only first-order derivative of the function appears in their proposed scheme. In this study, we have shown that the local convergence of these methods depends on hypotheses only on the first-order derivative and the Lipschitz condition. In this way, we not only expand the applicability of these methods but also proposed the theoretical radius of convergence of these methods. Finally, a variety of concrete numerical examples demonstrate that our results even apply to solve those nonlinear equations where earlier studies cannot apply." @default.
• W2955740789 created "2019-07-12" @default.
• W2955740789 creator A5065116244 @default.
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• W2955740789 date "2019-07-31" @default.
• W2955740789 modified "2023-09-27" @default.
• W2955740789 title "Ball Convergence for a Multi-Step Harmonic Mean Newton-Like Method in Banach Space" @default.
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• W2955740789 doi "https://doi.org/10.1142/s0219876219400188" @default.
• W2955740789 hasPublicationYear "2019" @default.
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