Argyros, I.K.George, S.2020-03-312020-03-312015Journal of Nonlinear Science and Applications, 2015, Vol.8, 3, pp.246-254https://idr.nitk.ac.in/handle/123456789/11917We present a local convergence analysis for deformed Halley method in order to approximate a solution of a nonlinear equation in a Banach space setting. Our methods include the Halley and other high order methods under hypotheses up to the first Fr chet-derivative in contrast to earlier studies using hypotheses up to the second or third Fr chet-derivative. The convergence ball and error estimates are given for these methods. Numerical examples are also provided in this study. 2015, International Scientific Research Publications. All rights reserved.Article