On Newton's method under mild differentiability conditions and applications (Q1294206)

This paper deals with the convergence of the Newton-Kantorovich method for approximating a locally unique solution of nonlinear operator defined on a convex subset of a Banach space by assuming that the Fréchet-derivative of this operator is only Hölder continuous. The author use this study to counter some claims made by \textit{A. Galperin} and \textit{Z. Waksman} [J. Comput. Appl. Math. 35, No. 1-3, 207-215 (1991; Zbl 0755.65057); Numer. Funct. Anal. Optimization 15, No. 7-8, 813-858 (1994; Zbl 0814.65054)] about the applicability of results in his earlier paper [Bull. Aust. Math. Soc. 38, No. 1, 131-140 (1988; Zbl 0642.65043)]. Furthermore the author uses obtained results to solve a nonlinear Chandrasehkar integral equation.