%0 Journal Article %T Local Convergence for a Family of Sixth Order Chebyshev-Halley-Type Methods in Banach Space Under Weak Conditions %J Khayyam Journal of Mathematics %I Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures) %Z 2423-4788 %A Argyros, Ioannis K. %A George, Santhosh %D 2018 %\ 01/01/2018 %V 4 %N 1 %P 1-12 %! Local Convergence for a Family of Sixth Order Chebyshev-Halley-Type Methods in Banach Space Under Weak Conditions %K Chebyshev-Halley method %K Banach space %K local convergence %K radius of convergence %K Fréchet-derivative %R 10.22034/kjm.2017.51873 %X 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. %U https://www.kjm-math.org/article_51873_01211642c310828d7695de3477fc151d.pdf