Argyros, I.K.George, S.2026-02-052016Communications on Applied Nonlinear Analysis, 2016, 23, 4, pp. 72-811074133Xhttps://idr.nitk.ac.in/handle/123456789/25898We present a unified local convergence analysis for inverse free Jarratttype method in order to approximate a solution of a nonlinear equation in a Banach space setting. Our methods include the Jarratt and Newton methods. The convergence ball and error estimates are given for these methods using Holder hypotheses up to the first Fréchet derivative. Earlier studies such as [?]-[?] have used the third Fréchet derivative. Numerical examples are also provided in this study.Banach spaceConvergence ballInexact Newton methodJarratt-type methodsLocal convergence