A unified local convergence for Chebyshev-Halley-type methods in Banach space under weak conditions
Keywords:
Chebyshev-Halley-type methods, Banach space, convergence ball, local convergence.Abstract
We present a unified local convergence analysis for Chebyshev-Halley- type methods in order to approximate a solution of a nonlinear equation in a Banach space setting. Our methods include the Chebyshev; Halley; super-Halley and other high order methods. The convergence ball and error estimates are given for these methods under the same conditions. Numerical examples are also provided in this study.
Mathematics Subject Classification (2010): 65D10, 65D99, 65G99, 47H17, 49M15.
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