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Journal of Applied Mathematics
Volume 2014, Article ID 468694, 8 pages
http://dx.doi.org/10.1155/2014/468694
Research Article

Convergence Theorem for a Family of New Modified Halley’s Method in Banach Space

1Department of Mathematics, Taizhou University, Linhai, Zhejiang 317000, China
2Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, China
3Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China

Received 18 February 2014; Revised 8 May 2014; Accepted 22 May 2014; Published 17 June 2014

Academic Editor: Alicia Cordero

Copyright © 2014 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

We establish convergence theorems of Newton-Kantorovich type for a family of new modified Halley’s method in Banach space to solve nonlinear operator equations. We present the corresponding error estimate. To show the application of our theorems, two numerical examples are given.