The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (242 KB) | Metadata | Table of Contents | ZAA summary
Volume 35, Issue 3, 2016, pp. 309–331
DOI: 10.4171/ZAA/1567

Published online: 2016-09-13

A Modification of the Lipschitz Condition in the Newton–Kantorovich Theorem

José Antonio Ezquerro[1] and Miguel Ángel Hernández-Verón[2]

(1) Universidad de la Rioja, Logrono, Spain
(2) Universidad de la Rioja, Logrono - La Rioja, Spain

We analyse the semilocal convergence of Newton’s method in Banach spaces under a modification of the classic Lipschitz condition on the first derivative of the operator involved in Kantorovich’s theory. For this, we use a technique based on recurrence relations instead of the well-known majorant principle of Kantorovich. We illustrate this analysis with an application where a Hammerstein nonlinear integral equation of the second kind is involved.

Keywords: Newton’s method, semilocal convergence, the Newton-Kantorovich theorem, recurrence relations, error estimates, order of convergence, nonlinear integral equation

Ezquerro José Antonio, Hernández-Verón Miguel Ángel: A Modification of the Lipschitz Condition in the Newton–Kantorovich Theorem. Z. Anal. Anwend. 35 (2016), 309-331. doi: 10.4171/ZAA/1567