On a sixth-order Jarratt-type method in Banach spaces

Abstract

We present a local convergence analysis of a sixth-order Jarratt-type method 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 such as [X. Wang, J. Kou and C. Gu, Semilocal convergence of a sixth-order Jarratt method in Banach spaces, Numer. Algorithms 57 (2011) 441-456.] require hypotheses up to the third Fr chet-derivative. Numerical examples are also provided in this study. 2015 World Scientific Publishing Company.