Auxiliary point on the semilocal convergence of Newton's method

Resumen

We use an auxiliary point on the semilocal convergence of Newton's method when the majorant principle of Kantorovich is applied to operators with high order derivatives satisfying a center Lipschitz type condition, so that we extend the classical conditions of these types, that are centered at the starting point of Newton's method, to other points belonging to the domain of definition of the operator involved. This extension provides a modification of the domain of starting points for Newton's method which allows increasing the choice of starting points. We illustrate this study with nonlinear Fredholm integral equations. © 2018 Elsevier B.V.