Argyros, I.K.Khattri, S.K.George, S.2026-02-052019Journal of Fixed Point Theory and Applications, 2019, 21, 1, pp. -16617738https://doi.org/10.1007/s11784-019-0662-6https://idr.nitk.ac.in/handle/123456789/24667We present a local convergence analysis of an at least sixth-order family of methods to approximate a locally unique solution of nonlinear equations in a Banach space setting. The semilocal convergence analysis of this method was studied by Amat et al. in (Appl Math Comput 206:164–174, 2008; Appl Numer Math 62:833–841, 2012). This work provides computable convergence ball and computable error bounds. Numerical examples are also provided in this study. © 2019, Springer Nature Switzerland AG.Banach spacelocal convergencemajorizing sequencesNewton-like methodsrecurrent functionsrecurrent relationsSixth-order methodsthree-step