On the convergence of the Newton-Kantorovich method: The generalized Holder case

Abstract

We provide a finer semilocal convergence analysis for the Newton-Kantorovich method than before [1], [5], [8]-[10] using more precise majorizing sequences in order to approximate a locally unique solution of an equation in a Banach space. It turns out that under the same or weaker hypotheses we can provide finer error bounds on the distances involved and a more precise information on the location of the solution.