Local convergence of deformed Jarratt-type methods in Banach space without inverses

Abstract

We present a local convergence analysis for the Jarratt-type method of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first Fr chet-derivative of the operator involved. Earlier studies use hypotheses up to the third Fr chet-derivative. Hence, the applicability of these methods is expanded under weaker hypotheses and less computational cost for the constants involved in the convergence analysis. Numerical examples are also provided in this study. World Scientific Publishing Company.