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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 923898, 8 pages
http://dx.doi.org/10.1155/2013/923898
Research Article

Newton-Kantorovich and Smale Uniform Type Convergence Theorem for a Deformed Newton Method in Banach Spaces

1Department of Mathematics, Taizhou University, Linhai, Zhejiang 317000, China
2Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technicka 8, 616 00 Brno, Czech Republic
3Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, China

Received 12 September 2013; Accepted 18 November 2013

Academic Editor: Miroslava Růžičková

Copyright © 2013 Rongfei Lin 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

Newton-Kantorovich and Smale uniform type of convergence theorem of a deformed Newton method having the third-order convergence is established in a Banach space for solving nonlinear equations. The error estimate is determined to demonstrate the efficiency of our approach. The obtained results are illustrated with three examples.