Ball Convergence for an Inverse Free Jarratt-Type Method Under H lder 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 Fr chet-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 Fr chet derivative under H lder conditions. This way we expand the applicability of the method. Numerical examples are also provided in this study. 2015, Springer India Pvt. Ltd.