Argyros, I.K.George, S.2020-03-312020-03-312017Revista Colombiana de Matematicas, 2017, Vol.51, 1, pp.1-14https://idr.nitk.ac.in/handle/123456789/10044We present a local convergence analysis for a family of Steffensen- type third-order methods in order to approximate a solution of a nonlinear equation. We use hypothesis up to the first derivative in contrast to earlier studies such as [2, 4, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28] using hypotheses up to the fourth derivative. This way the applicability of these methods is extended under weaker hypothesis. More- over 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.Article