On a unified convergence analysis for Newton-type methods solving generalized equations with the Aubin property

Abstract

A 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.