Argyros, I.K.George, S.2026-02-052015Journal of Nonlinear Science and Applications, 2015, 8, 3, pp. 246-25420081898https://doi.org/10.22436/jnsa.008.03.09https://idr.nitk.ac.in/handle/123456789/26254We 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 Fréchet-derivative in contrast to earlier studies using hypotheses up to the second or third Fréchet-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.Banach spaceChebyshev methodConvergence ballLocal convergence