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

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.

Keywords:

• deformed Newton's method
• Banach space
• nonlinear equation
• Newton–Kantorovich theorem
• γ-condition

2000 AMS Subject Classification :

• 65J15
• 47J25
• 47J05
• 65H10
• 65J05

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).