Argyros, I.K.George, S.2026-02-052021Serdica Mathematical Journal, 2021, 47, 2, pp. 93-10613106600https://doi.org/10.55630/serdica.2021.47.93-106https://idr.nitk.ac.in/handle/123456789/23195The convergence region of iterative procedures is small in general, and it becomes smaller as m increases. This problem limits the choice of starting points, and consequently the applicability of these methods. The novelty of this work lies in the fact that, we extend the convergence region by using specializations of the Lipschitz constants used before. Further advantages include improved error estimations and uniqueness results. The results are tested favorably to us on examples. © 2021, Bulgarian Academy of Sciences, Institute of Mathematics and Informatics. All rights reserved.Banach spaceLipschitz continuitym-step iterative methodsNewton’s methodsemi-local convergence