Argyros, I.K.George, S.2026-02-042024Journal of Complexity, 2024, 81, , pp. -0885064Xhttps://doi.org/10.1016/j.jco.2023.101817https://idr.nitk.ac.in/handle/123456789/21216A plethora of applications from diverse disciplines reduce to solving generalized equations involving Banach space valued operators. These equations are solved mostly iteratively, when a sequence is generated approximating a solution provided that certain conditions are valid on the starting point and the operators appearing on the method. Secant-type methods are developed whose specializations reduce to well known methods such as Newton, modified Newton, Secant, Kurchatov and Steffensen to mention a few. Unified local as well as semi-local analysis of these methods is presented using the celebrated contraction mapping principle in combination with the Aubin property of a set valued operator, and generalized continuity assumption on the operators on these methods. Numerical applications complement the theory. © 2023 Elsevier Inc.Newton-Raphson methodAubin propertiesConditionConvergence analysisGeneralized EquationsLocal-semi-local convergenceNewton's methodsNewton-type methodsSecant-type methodsSemilocal convergenceSpecialisationBanach spaces