Implicit Function Theorem. Part I

Pole DC	Wartość	Język
dc.contributor.author	Nakasho, Kazuhisa	-
dc.contributor.author	Futa, Yuichi	-
dc.contributor.author	Shidama, Yasunari	-
dc.date.accessioned	2018-05-11T07:20:21Z	-
dc.date.available	2018-05-11T07:20:21Z	-
dc.date.issued	2017	-
dc.identifier.citation	Formalized Mathematics, Volume 25, Issue 4, Pages 269–281	-
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/6552	-
dc.description.abstract	In this article, we formalize in Mizar [1], [3] the existence and uniqueness part of the implicit function theorem. In the first section, some composition properties of Lipschitz continuous linear function are discussed. In the second section, a definition of closed ball and theorems of several properties of open and closed sets in Banach space are described. In the last section, we formalized the existence and uniqueness of continuous implicit function in Banach space using Banach fixed point theorem. We referred to [7], [8], and [2] in this formalization.	-
dc.description.sponsorship	This study was supported in part by JSPS KAKENHI Grant Number JP17K00182	pl
dc.language.iso	en	-
dc.publisher	DeGruyter Open	-
dc.subject	implicit function theorem	-
dc.subject	Banach fixed point theorem	-
dc.subject	Lipschitz continuity	-
dc.title	Implicit Function Theorem. Part I	-
dc.type	Article	-
dc.identifier.doi	10.1515/forma-2017-0026	-
dc.description.Affiliation	Nakasho Kazuhisa - Osaka University, Osaka, Japan	-
dc.description.Affiliation	Futa Yuichi - Tokyo University of Technology, Tokyo, Japan	-
dc.description.Affiliation	Shidama Yasunari - Shinshu University, Nagano, Japan	-
dc.description.references	Grzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pak, 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.	-
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dc.description.references	Hideki Sakurai, Hiroyuki Okazaki, and Yasunari Shidama. Banach’s continuous inverse theorem and closed graph theorem. Formalized Mathematics, 20(4):271-274, 2012. doi: 10.2478/v10037-012-0032-y.	-
dc.description.references	Laurent Schwartz. Théorie des ensembles et topologie, tome 1. Analyse. Hermann, 1997.	-
dc.description.references	Laurent Schwartz. Calcul différentiel, tome 2. Analyse. Hermann, 1997.Google Scholar	-
dc.description.references	Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.	-
dc.identifier.eissn	1898-9934	-
dc.description.volume	25	-
dc.description.issue	4	-
dc.description.firstpage	269	-
dc.description.lastpage	281	-
dc.identifier.citation2	Formalized Mathematics	-
Występuje w kolekcji(ach):	Formalized Mathematics, 2017, Volume 25, Issue 4

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