Ball Convergence for an Inverse Free Jarratt-Type Method Under Hölder Conditions

Abstract

We present a local convergence analysis of an inverse free Jarratt-type method in order to approximate a locally unique solution of an equation in a Banach space setting. Earlier studies have used hypotheses up to the third Fréchet-derivative of the operator involved to show convergence although only the first derivative is used in the method. We show convergence using only the first Fréchet derivative under Hölder conditions. This way we expand the applicability of the method. Numerical examples are also provided in this study. © 2015, Springer India Pvt. Ltd.