On Implicit and Inverse Function Theorems on Euclidean Spaces

Kazuhisa Nakasho; Yasunari Shidama

doi:10.2478/forma-2022-0012

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On Implicit and Inverse Function Theorems on Euclidean Spaces

Formalized Mathematics

Volume 30 (2022): Issue 3 (October 2022)

By: Kazuhisa Nakasho and Yasunari Shidama

Open Access

|Dec 2022

Abstract

Previous Mizar articles [7, 6, 5] formalized the implicit and inverse function theorems for Frechet continuously differentiable maps on Banach spaces. In this paper, using the Mizar system [1], [2], we formalize these theorems on Euclidean spaces by specializing them. We referred to [4], [12], [10], [11] in this formalization.

References

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Articles in this issue

DOI: https://doi.org/10.2478/forma-2022-0012 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630

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Language: English

Page range: 159 - 168

Accepted on: Sep 30, 2022

Published on: Dec 30, 2022

Published by: University of Białystok

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

implicit function theorem,

inverse function theorem,

continuously differentiable function

Related subjects:

Computer sciences,

Computer sciences, other,

Mathematics,

General mathematics

© 2022 Kazuhisa Nakasho, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.

Volume 30 (2022): Issue 3 (October 2022)