A modification of the Lipschitz condition in the Newton-Kantorovich theorem
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Universidad de La Rioja
info
ISSN: 0232-2064
Argitalpen urtea: 2016
Alea: 35
Zenbakia: 3
Orrialdeak: 309-331
Mota: Artikulua
Beste argitalpen batzuk: Zeitschrift für Analysis und ihre Anwendungen
Lotura duten proiektuak
Laburpena
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.