Argyros, I.K.George, S.2026-02-052018Khayyam Journal of Mathematics, 2018, 4, 1, pp. 1-12https://doi.org/10.22034/kjm.2017.51873https://idr.nitk.ac.in/handle/123456789/25324We 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.Banach spaceChebyshev-Halley methodFréchet-derivativeLocal convergenceRadius of convergence