Argyros, I.K.George, S.2026-02-052017Revista Colombiana de Matematicas, 2017, 51, 1, pp. 1-14347426https://doi.org/10.15446/recolma.v51n1.66831https://idr.nitk.ac.in/handle/123456789/25754We 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.Local convergenceNewton's methodOrder of convergenceSteffensen's method