Abstract
The paper is concerned with the application of Kantorovich-type majorants for the convergence of Newton’s method to a locally unique solution of a nonlinear equation in a Banach space setting. The Fréchet-derivative of the operator involved satisfies only a rather weak continuity condition. Using our new idea of recurrent functions, we obtain sufficient convergence conditions, as well as error estimates. The results compare favorably to earlier ones (Ezquerro, Hernández in IMA J. Numer. Anal. 22:187–205, 2002 and Proinov in J. Complex. 26:3–42, 2010).
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Argyros, I.K., Hilout, S. Newton–Kantorovich approximations under weak continuity conditions. J. Appl. Math. Comput. 37, 361–375 (2011). https://doi.org/10.1007/s12190-010-0439-y
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DOI: https://doi.org/10.1007/s12190-010-0439-y