Argyros, I.K.Cho, Y.J.George, S.2020-03-312020-03-312014Journal of the Korean Mathematical Society, 2014, Vol.51, 2, pp.251-266https://idr.nitk.ac.in/handle/123456789/12370In 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 Fr chet-derivative of the operator involved is p-H lder continuous (p ?(0, 1]). Numerical examples involving two boundary value problems are also provided. 2014 Korean Mathematical Society.Article