Argyros I.K.George S.2021-05-052021-05-052020Panamerican Mathematical Journal , Vol. 30 , 3 , p. 35 - 50https://doi.org/https://idr.nitk.ac.in/handle/123456789/15282In this study a convergence analysis for a fast multi-step Chebyshe-Halley-type method for solving nonlinear equations involving Banach space valued operator is presented. We introduce a more precise convergence region containing the iterates leading to tighter Lipschitz constants and functions. This way advantages are obtained in both the local as well as the semi-local convergence case under the same computational cost such as: extended convergence domain, tighter error bounds on the distances involved and a more precise in-formation on the location of the solution. The new technique can be used to extend the applicability of other iterative methods. The numerical examples further validate the theoretical results. © 2020, International Publications. All rights reserved.Article