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Abstract and Applied Analysis
Volume 2012, Article ID 982925, 13 pages
Research Article

Semilocal Convergence Analysis for Inexact Newton Method under Weak Condition

Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China

Received 29 May 2012; Accepted 5 August 2012

Academic Editor: Jen-Chih Yao

Copyright © 2012 Xiubin Xu 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.


Under the hypothesis that the first derivative satisfies some kind of weak Lipschitz conditions, a new semilocal convergence theorem for inexact Newton method is presented. Unified convergence criteria ensuring the convergence of inexact Newton method are also established. Applications to some special cases such as the Kantorovich type conditions and 𝛾-Conditions are provided and some well-known convergence theorems for Newton's method are obtained as corollaries.