Higher-Order Differentiation and Inverse Function Theorem in Real Normed Spaces
By: Kazuhisa Nakasho
and Yasunari Shidama
and Yasunari Shidama References
- Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.
- Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.
- Nelson Dunford and Jacob T. Schwartz. Linear operators I. Interscience Publ., 1958.
- Noboru Endou and Yasunari Shidama. Differentiation in normed spaces. Formalized Mathematics, 21(2):95–102, 2013. doi:10.2478/forma-2013-0011.
- Isao Miyadera. Functional Analysis. Riko-Gaku-Sya, 1972.
- Kazuhisa Nakasho. Invertible operators on Banach spaces. Formalized Mathematics, 27 (2):107–115, 2019. doi:10.2478/forma-2019-0012.
- Kazuhisa Nakasho and Yasunari Shidama. On implicit and inverse function theorems on Euclidean spaces. Formalized Mathematics, 30(3):159–168, 2022. doi:10.2478/forma-2022-0012.
- Kazuhisa Nakasho and Yasunari Shidama. Differentiability properties of Lipschitzian bilinear operators in real normed spaces. Formalized Mathematics, 32(1):165–172, 2024. doi:10.2478/forma-2024-0013.
- Hiroyuki Okazaki, Noboru Endou, and Yasunari Shidama. Cartesian products of family of real linear spaces. Formalized Mathematics, 19(1):51–59, 2011. doi:10.2478/v10037-011-0009-2.
- Laurent Schwartz. Théorie des ensembles et topologie, tome 1. Analyse. Hermann, 1997.
- Laurent Schwartz. Calcul différentiel, tome 2. Analyse. Hermann, 1997.
- Kôsaku Yosida. Functional Analysis. Springer, 1980.
Language: English
Page range: 247 - 269
Accepted on: Dec 24, 2024
Published on: Dec 31, 2024
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
Related subjects:
© 2024 Kazuhisa Nakasho, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License.