Higher-Order Differentiation and Inverse Function Theorem in Real Normed Spaces

[1]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.Open DOISearch in Google Scholar

[2]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.Open DOISearch in Google Scholar

[3]Nelson Dunford and Jacob T. Schwartz. Linear operators I. Interscience Publ., 1958.Search in Google Scholar

[4]Noboru Endou and Yasunari Shidama. Differentiation in normed spaces. Formalized Mathematics, 21(2):95–102, 2013. doi:10.2478/forma-2013-0011.Open DOISearch in Google Scholar

[5]Isao Miyadera. Functional Analysis. Riko-Gaku-Sya, 1972.Search in Google Scholar

[6]Kazuhisa Nakasho. Invertible operators on Banach spaces. Formalized Mathematics, 27 (2):107–115, 2019. doi:10.2478/forma-2019-0012.Open DOISearch in Google Scholar

[7]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.Open DOISearch in Google Scholar

[8]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.Open DOISearch in Google Scholar

[9]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.Open DOISearch in Google Scholar

[10]Laurent Schwartz. Théorie des ensembles et topologie, tome 1. Analyse. Hermann, 1997.Search in Google Scholar

[11]Laurent Schwartz. Calcul différentiel, tome 2. Analyse. Hermann, 1997.Search in Google Scholar

[12]Kôsaku Yosida. Functional Analysis. Springer, 1980.Search in Google Scholar