| Article ID: | iaor20128586 |
| Volume: | 57 |
| Issue: | 3-4 |
| Start Page Number: | 584 |
| End Page Number: | 594 |
| Publication Date: | Feb 2013 |
| Journal: | Mathematical and Computer Modelling |
| Authors: | Ezquerro J A, Gonzlez D, Hernndez M A |
| Keywords: | Newton method, Banach space |
We study the semilocal convergence of Newton’s method in Banach spaces under a modification of the classic conditions of Kantorovich, which leads to a generalization of Kantorovich’s theory. We illustrate this study with two Hammerstein integral equations of the second kind, where the classic conditions of Kantorovich cannot be applied, but our modification of them can.