A variant of the Newton-Kantorovich theorem for nonlinear integral equations of mixed Hammerstein type
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Universidad de La Rioja
info
ISSN: 0096-3003
Any de publicació: 2012
Volum: 218
Número: 18
Pàgines: 9536-9546
Tipus: Article
Altres publicacions en: Applied Mathematics and Computation
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Resum
We study nonlinear integral equations of mixed Hammerstein type using Newton's method as follows. We investigate the theoretical significance of Newton's method to draw conclusions about the existence and uniqueness of solutions of these equations. After that, we approximate the solutions of a particular nonlinear integral equation by Newton's method. For this, we use the majorant principle, which is based on the concept of majorizing sequence given by Kantorovich, and milder convergence conditions than those of Kantorovich. Actually, we prove a semilocal convergence theorem which is applicable to situations where Kantorovich's theorem is not. © 2012 Elsevier Inc. All rights reserved.