Argyros, I.K.George, S.2026-02-052020Panamerican Mathematical Journal, 2020, 30, 3, pp. 35-5010649735https://idr.nitk.ac.in/handle/123456789/23831In 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.Chebyshev methodConvergence orderHalley methodLocalMulti-step methodSemi-local convergence