Concerning the convergence of Newton-like methods under weak Hölder continuity conditions

Abstract

The concept of majorizing sequences is employed to provide a convergence analysis for Newton-like methods in a Banach space. We use Hölder and center-Hölder continuity assumptions on the Fréchet-derivative of the operators involved. This way we show that our convergence conditions are weaker; error bounds on the distances involved finer and the location of the solution more precise than in earlier results.