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.
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).