A modification of the Lipschitz condition in the Newton-Kantorovich theorem
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Universidad de La Rioja
info
ISSN: 0232-2064
Year of publication: 2016
Volume: 35
Issue: 3
Pages: 309-331
Type: Article
More publications in: Zeitschrift für Analysis und ihre Anwendungen
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Abstract
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.