Abstract
A Newton–Kantorovich convergence theorem of a modified Newton’s method having third order convergence is established under the gamma-condition in a Banach space to solve nonlinear equations. It is assumed that the nonlinear operator is twice Fréchet differentiable and satisfies the gamma-condition. We also present the error estimate to demonstrate the efficiency of our approach. A comparison of our numerical results with those obtained by other Newton–Kantorovich convergence theorems shows high accuracy of our results.
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Communicated by Ilio Galligani.
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Chen, M., Khan, Y., Wu, Q. et al. Newton–Kantorovich Convergence Theorem of a Modified Newton’s Method Under the Gamma-Condition in a Banach Space. J Optim Theory Appl 157, 651–662 (2013). https://doi.org/10.1007/s10957-012-0237-9
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DOI: https://doi.org/10.1007/s10957-012-0237-9