Local convergence for a family of sixth order Chebyshev-Halley -type methods in Banach space under weak conditions

Abstract

We present a local convergence analysis for a family of super- Halley methods 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 and second Fréchet-derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet derivative. Numerical examples are also provided in this study. © 2017 Khayyam Journal of Mathematics.