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ABSTRACT
In this paper, our efforts are dedicated to study the application of Newton's method to a fully parameterized generalized equation in which both single-valued and set-valued functions depend on the parameter. We established results concerning parametric properties of the associated sequences of Newton's iterates, which follows the general format of the implicit function theorem paradigm.
Acknowledgements
The authors are grateful to the referees and editors for their helpful comments and constructive suggestions which helped us to improve the quality of this work.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Funding
W. Ouyang's research was supported by the National Natural Science Foundation of the People's Republic of China [grant numbers 11801500, 61663049] and the Yunnan Provincial Science and Technology Research Program [grant number 2017FD070]. B. Zhang's research was supported by the National Natural Science Foundation of the People's Republic of China [grant numbers 11461080, 11771384].