A modification of the Lipschitz condition in the Newton-Kantorovich theorem
-
1
Universidad de La Rioja
info
ISSN: 0232-2064
Datum der Publikation: 2016
Ausgabe: 35
Nummer: 3
Seiten: 309-331
Art: Artikel
Andere Publikationen in: Zeitschrift für Analysis und ihre Anwendungen
Projekte im Zusammenhang
Zusammenfassung
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. © European Mathematical Society.