A NOTE ON THE IMPROVEMENT OF THE ERROR BOUNDS FOR A CERTAIN CLASS OF OPERATORS

Abstract

We use Newton's method to approximate a locally unique solution of an equation in a Banach space setting. We show that our error bounds on the distances involved can be tighter than before [6]{[12], under new sucient convergence conditions, provided that the Fr{\'e}chet-derivative of the operator involved is p-H{\"o}lder continuous, where p in (0, 1]. Numerical examples validating our result are given at the end of this study.