Some methods for finding error bounds for Newton-like methods under mild differentiability conditions
The author extends convergence results of \textit{T. Yamamoto} [Numer. Math. 51, 545-557 (1987; Zbl 0633.65049)] for iterative methods of Newton-type applied to the solution of nonlinear equations \(F(x) = 0\) in Banach spaces. In particular, the Lipschitz condition for the derivative of \(F\) used by Yamamoto is replaced by a Hölder condition.
scientific article; zbMATH DE number 508713