Argyros, I.K.George, S.2026-02-052016Rendiconti del Circolo Matematico di Palermo, 2016, 65, 1, pp. 87-960009725Xhttps://doi.org/10.1007/s12215-015-0220-zhttps://idr.nitk.ac.in/handle/123456789/26029We present a local convergence analysis for Euler–Halley-like methods with a parameter in order to approximate a locally unique solution of an equation in a Banach space setting. Using more flexible Lipschitz-type hypotheses than in earlier studies such as Huang and Ma (Numer Algorith 52:419–433, 2009), we obtain a larger radius of convergence as well as more precise error estimates on the distances involved. Numerical examples justify our theoretical results. © 2015, Springer-Verlag Italia.Banach spaceEuler methodGeneralized Lipschitz/center-Lipschitz conditionHalley methodLocal convergence