Argyros, I.K.George, S.2026-02-052021Journal of Numerical Analysis and Approximation Theory, 2021, 50, 1, pp. 44-5124576794https://doi.org/10.33993/jnaat501-1247https://idr.nitk.ac.in/handle/123456789/22993We present a local convergence analysis Potra-Ptak-type method with optimal fourth order of convergence in order to approximate a solution of a nonlinear equation. In earlier studies such as [1], [5]–[28] hypotheses up to the fourth derivative are used. In this paper we use hypotheses up to the first derivative only, so that the applicability of these methods is extended under weaker hypotheses. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study. © 2021, Publishing House of the Romanian Academy. All rights reserved.local convergenceNewton’s methodorder of convergencePotra-Ptak-type method