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Section B

Convergence analysis for a deformed Newton's method with third-order in Banach space under γ-condition

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Pages 441-450 | Received 20 Jan 2006, Accepted 25 Jul 2007, Published online: 21 Feb 2009
 

Abstract

We establish the Newton–Kantorovich convergence theorem for a deformed Newton's method in Banach space under γ-condition, which is used to solve the nonlinear equation. We also present the error estimate. Finally, some examples are provided to show the application of our theorem.

2000 AMS Subject Classification :

Acknowledgements

The authors thank editors and the anonymous referee for his/her careful reading and many valuable comments on improving the original manuscript. This work is supported by Natural Science Foundation of Zhejiang Province (Grant No. Y606154).

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