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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 682167, 11 pages
http://dx.doi.org/10.1155/2013/682167
Research Article

Convergence Behavior for Newton-Steffensen’s Method under -Condition of Second Derivative

1Department of Mathematics, Zhejiang University, Hangzhou 310027, China
2Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

Received 2 September 2013; Accepted 30 September 2013

Academic Editor: Jen-Chih Yao

Copyright © 2013 Yonghui Ling 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

The present paper is concerned with the semilocal as well as the local convergence problems of Newton-Steffensen’s method to solve nonlinear operator equations in Banach spaces. Under the assumption that the second derivative of the operator satisfies -condition, the convergence criterion and convergence ball for Newton-Steffensen’s method are established.