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 Frechet-derivative of the operator involved. Earlier studies use hypotheses up to the third Frechet-derivative. Numerical examples are also provided in this study.