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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 782170, 14 pages
http://dx.doi.org/10.1155/2012/782170
Research Article

On a Family of High-Order Iterative Methods under Kantorovich Conditions and Some Applications

1Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 30203 Cartagena, Spain
2Departamento de Matemáticas, Facultad de Ciencias, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile

Received 23 February 2012; Revised 4 June 2012; Accepted 4 June 2012

Academic Editor: John Rassias

Copyright © 2012 S. Amat et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is devoted to the study of a class of high-order iterative methods for nonlinear equations on Banach spaces. An analysis of the convergence under Kantorovich-type conditions is proposed. Some numerical experiments, where the analyzed methods present better behavior than some classical schemes, are presented. These applications include the approximation of some quadratic and integral equations.