Argyros, I.K.Cho, Y.J.George, S.2026-02-052014Journal of the Korean Mathematical Society, 2014, 51, 2, pp. 251-2663049914https://doi.org/10.4134/JKMS.2014.51.2.251https://idr.nitk.ac.in/handle/123456789/26516In this paper, we use Newton's method to approximate a locally unique solution of an equation in Banach spaces and introduce recurrent functions to provide a weaker semilocal convergence analysis for Newton's method than before [1]-[13], in some interesting cases, provided that the Fréchet-derivative of the operator involved is p-Hölder continuous (p ?(0, 1]). Numerical examples involving two boundary value problems are also provided. © 2014 Korean Mathematical Society.Banach spaceDifferential equationHölder continuityLipschitz continuityNewton's methodNewton-kantorovich hypothesisRecurrent functionsSemilocal convergence