Argyros, I.K.George, S.2026-02-052017Asian-European Journal of Mathematics, 2017, 10, 2, pp. -17935571https://doi.org/10.1142/S1793557117500863https://idr.nitk.ac.in/handle/123456789/25621We present a unified local convergence analysis for deformed Euler-Halley-type methods in order to approximate a solution of a nonlinear equation in a Banach space setting. Our methods include the Euler, Halley and other high order methods. The convergence ball and error estimates are given for these methods under hypotheses up to the first Fréchet derivative in contrast to earlier studies using hypotheses up to the second Fréchet derivative. Numerical examples are also provided in this study. © 2017 World Scientific Publishing Company.Banach spaceChebyshev-Halley-type methodsconvergence balllocal convergence