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  4. Formalized Mathematics, 2024, Volume 32, Issue 1

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    • Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji: http://hdl.handle.net/11320/17781
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    Pole DCWartośćJęzyk
    dc.contributor.authorNakasho, Kazuhisa-
    dc.contributor.authorShidama, Yasunari-
    dc.date.accessioned2025-01-09T10:24:10Z-
    dc.date.available2025-01-09T10:24:10Z-
    dc.date.issued2024-
    dc.identifier.citationFormalized Mathematics, Volume 32, Issue 1, Pages 165–172pl
    dc.identifier.issn1426-2630-
    dc.identifier.urihttp://hdl.handle.net/11320/17781-
    dc.description.abstractThis article is devoted to the Mizar formalization of various properties of differentiability of Lipschitzian bilinear operators in real normed spaces. Main results include the Lipschitz continuity of partial derivatives, the representation of the total derivative in terms of partial derivatives, and the continuous differentiability of Lipschitzian bilinear operators on open subsets of the product space.pl
    dc.language.isoenpl
    dc.publisherDeGruyter Openpl
    dc.rightsAttribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)pl
    dc.rights.urihttps://creativecommons.org/licenses/by-sa/3.0/pl
    dc.subjectbilinear operatorpl
    dc.subjectLipschitz continuitypl
    dc.subjectnormed spacepl
    dc.titleDifferentiability Properties of Lipschitzian Bilinear Operators in Real Normed Spacespl
    dc.typeArticlepl
    dc.rights.holder© 2024 The Author(s)pl
    dc.rights.holderCC BY-SA 3.0 licensepl
    dc.identifier.doi10.2478/forma-2024-0013-
    dc.description.AffiliationKazuhisa Nakasho - Yamaguchi University, Yamaguchi, Japanpl
    dc.description.AffiliationYasunari Shidama - Karuizawa Hotch 244-1, Nagano, Japanpl
    dc.description.referencesGrzegorz 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.pl
    dc.description.referencesGrzegorz 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.pl
    dc.description.referencesNelson Dunford and Jacob T. Schwartz. Linear operators I. Interscience Publ., 1958.pl
    dc.description.referencesNoboru Endou and Yasunari Shidama. Differentiation in normed spaces. Formalized Mathematics, 21(2):95–102, 2013. doi:10.2478/forma-2013-0011.pl
    dc.description.referencesYuichi Futa, Noboru Endou, and Yasunari Shidama. Isometric differentiable functions on real normed space. Formalized Mathematics, 21(4):249–260, 2013. doi:10.2478/forma-2013-0027.pl
    dc.description.referencesIsao Miyadera. Functional Analysis. Riko-Gaku-Sya, 1972.pl
    dc.description.referencesKazuhisa Nakasho. Bilinear operators on normed linear spaces. Formalized Mathematics, 27(1):15–23, 2019. doi:10.2478/forma-2019-0002.pl
    dc.description.referencesKazuhisa Nakasho and Yuichi Futa. Isomorphism between spaces of multilinear maps and nested compositions over real normed vector spaces. Formalized Mathematics, 30(1): 67–77, 2022. doi:10.2478/forma-2022-0006.pl
    dc.description.referencesKazuhisa 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.pl
    dc.description.referencesKazuhisa Nakasho, Yuichi Futa, and Yasunari Shidama. Continuity of bounded linear operators on normed linear spaces. Formalized Mathematics, 26(3):231–237, 2018. doi:10.2478/forma-2018-0021.pl
    dc.description.referencesLaurent Schwartz. Theorie des ensembles et topologie, tome 1. Analyse. Hermann, 1997.pl
    dc.description.referencesLaurent Schwartz. Calcul differentiel, tome 2. Analyse. Hermann, 1997.pl
    dc.description.referencesKosaku Yosida. Functional Analysis. Springer, 1980.pl
    dc.identifier.eissn1898-9934-
    dc.description.volume32pl
    dc.description.issue1pl
    dc.description.firstpage165pl
    dc.description.lastpage172pl
    dc.identifier.citation2Formalized Mathematicspl
    dc.identifier.orcid0000-0003-1110-4342-
    Występuje w kolekcji(ach):Formalized Mathematics, 2024, Volume 32, Issue 1

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