TY - JOUR ID - 51873 TI - Local Convergence for a Family of Sixth Order Chebyshev-Halley-Type Methods in Banach Space Under Weak Conditions JO - Khayyam Journal of Mathematics JA - KJM LA - en SN - AU - Argyros, Ioannis K. AU - George, Santhosh AD - Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA. AD - Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India-575 025. Y1 - 2018 PY - 2018 VL - 4 IS - 1 SP - 1 EP - 12 KW - Chebyshev-Halley method KW - Banach space KW - local convergence KW - radius of convergence KW - Fréchet-derivative DO - 10.22034/kjm.2017.51873 N2 - 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. UR - https://www.kjm-math.org/article_51873.html L1 - https://www.kjm-math.org/article_51873_01211642c310828d7695de3477fc151d.pdf ER -