W BIAŁYMSTOKU
Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji:
http://hdl.handle.net/11320/19656Pełny rekord metadanych
| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Nakasho, Kazuhisa | - |
| dc.contributor.author | Shidama, Yasunari | - |
| dc.date.accessioned | 2026-01-26T13:23:54Z | - |
| dc.date.available | 2026-01-26T13:23:54Z | - |
| dc.date.issued | 2025 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 33, Issue 1, Pages 103-115 | pl |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/19656 | - |
| dc.description.abstract | This article formalizes higher-order partial differentiable functions in Mizar: it introduces the concept of partial differentiation for functions between real normed spaces and develops the theory of partial derivatives of arbitrary order. Key results include properties of partial derivatives, their relationship with total derivatives, and criteria for the continuity of higher-order partial derivatives. | pl |
| dc.language.iso | en | pl |
| dc.publisher | University of Białystok | pl |
| dc.rights | Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) | pl |
| dc.rights.uri | https://creativecommons.org/licenses/by-sa/4.0/ | pl |
| dc.subject | partial differentiation | pl |
| dc.subject | higher-order derivative | pl |
| dc.subject | continuously differentiable function | pl |
| dc.title | Higher Order Partial Differentiable Functions | pl |
| dc.type | Article | pl |
| dc.rights.holder | 2025 The Author(s) | pl |
| dc.rights.holder | CC BY-SA 4.0 license | pl |
| dc.identifier.doi | 10.2478/forma-2025-0009 | - |
| dc.description.Affiliation | Kazuhisa Nakasho - Yamaguchi University, Yamaguchi, Japan | pl |
| dc.description.Affiliation | Yasunari Shidama - Karuizawa Hotch 244-1, Nagano, Japan | pl |
| dc.description.references | Nelson Dunford and Jacob T. Schwartz. Linear operators I. Interscience Publ., 1958. | pl |
| dc.description.references | Noboru Endou and Yasunari Shidama. Differentiation in normed spaces. Formalized Mathematics, 21(2):95–102, 2013. doi:10.2478/forma-2013-0011. | pl |
| dc.description.references | Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Mizar in a nutshell. Journal of Formalized Reasoning, 3(2):153–245, 2010. | pl |
| dc.description.references | Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1. | pl |
| dc.description.references | Isao Miyadera. Functional Analysis. Riko-Gaku-Sya, 1972. | pl |
| dc.description.references | Kazuhisa Nakasho and Yasunari Shidama. Higher-order differentiation and inverse function theorem in real normed spaces. Formalized Mathematics, 32(1):247–269, 2024. doi:10.2478/forma-2024-0021. | pl |
| dc.description.references | Laurent Schwartz. Theorie des ensembles et topologie, tome 1. Analyse. Hermann, 1997. | pl |
| dc.description.references | Laurent Schwartz. Calcul differentiel, tome 2. Analyse. Hermann, 1997. | pl |
| dc.description.references | Yasunari Shidama. Differentiable functions on normed linear spaces. Formalized Mathematics, 20(1):31–40, 2012. doi:10.2478/v10037-012-0005-1. | pl |
| dc.description.references | Kosaku Yosida. Functional Analysis. Springer, 1980. | pl |
| dc.identifier.eissn | 1898-9934 | - |
| dc.description.volume | 33 | pl |
| dc.description.issue | 1 | pl |
| dc.description.firstpage | 103 | pl |
| dc.description.lastpage | 115 | pl |
| dc.identifier.citation2 | Formalized Mathematics | pl |
| dc.identifier.orcid | 0000-0003-1110-4342 | - |
| Występuje w kolekcji(ach): | Formalized Mathematics, 2025, Volume 33, Issue 1 | |
Pliki w tej pozycji:
| Plik | Opis | Rozmiar | Format | |
|---|---|---|---|---|
| Higher_Order_Partial_Differentiable_Functions.pdf | 268,11 kB | Adobe PDF | Otwórz |
Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL
