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

作者：Antonio Ezquerro Jose; Angel Hernandez Veron Miguel

来源：Zeitschrift fur Analysis und Ihre Anwendungen, 2016, 35(3): 309-331.

DOI：10.4171/ZAA/1567

• Newton's method
• semilocal convergence
• the Newton-Kantorovich theorem
• recurrence relations
• error estimates
• order of convergence
• nonlinear integral equation

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.

• 出版日期2016