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http://hdl.handle.net/11320/3695Pełny rekord metadanych
| Pole DC | Wartość | Język |
|---|---|---|
| dc.contributor.author | Narita, Keiko | - |
| dc.contributor.author | Endou, Noboru | - |
| dc.contributor.author | Shidama, Yasunari | - |
| dc.date.accessioned | 2015-12-09T20:40:19Z | - |
| dc.date.available | 2015-12-09T20:40:19Z | - |
| dc.date.issued | 2013 | - |
| dc.identifier.citation | Formalized Mathematics, Volume 21, Issue 4, 2013, Pages 261-272 | - |
| dc.identifier.issn | 1426-2630 | - |
| dc.identifier.issn | 1898-9934 | - |
| dc.identifier.uri | http://hdl.handle.net/11320/3695 | - |
| dc.description.abstract | In this article, we describe the differential equations on functions from R into real Banach space. The descriptions are based on the article [20]. As preliminary to the proof of these theorems, we proved some properties of differentiable functions on real normed space. For the proof we referred to descriptions and theorems in the article [21] and the article [32]. And applying the theorems of Riemann integral introduced in the article [22], we proved the ordinary differential equations on real Banach space. We referred to the methods of proof in [30]. | - |
| dc.language.iso | en | - |
| dc.publisher | De Gruyter Open | - |
| dc.subject | formalization of differential equations | - |
| dc.title | Differential Equations on Functions from R into Real Banach Space | - |
| dc.type | Article | - |
| dc.identifier.doi | 10.2478/forma-2013-0028 | - |
| dc.description.Affiliation | Narita Keiko - Hirosaki-city Aomori, Japan | - |
| dc.description.Affiliation | Endou Noboru - Gifu National College of Technology Gifu, Japan | - |
| dc.description.Affiliation | Shidama Yasunari - Shinshu University Nagano, Japan | - |
| dc.description.references | Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. | - |
| dc.description.references | Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. | - |
| dc.description.references | Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. | - |
| dc.description.references | Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485-492, 1996. | - |
| dc.description.references | Czesław Bylinski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990. | - |
| dc.description.references | Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990. | - |
| dc.description.references | Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. | - |
| dc.description.references | Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. | - |
| dc.description.references | Czesław Bylinski. Introduction to real linear topological spaces. Formalized Mathematics, 13(1):99-107, 2005. | - |
| dc.description.references | Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. | - |
| dc.description.references | Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991. | - |
| dc.description.references | Noboru Endou and Yasunari Shidama. Completeness of the real Euclidean space. Formalized Mathematics, 13(4):577-580, 2005. | - |
| dc.description.references | Noboru Endou, Katsumi Wasaki, and Yasunari Shidama. Definition of integrability for partial functions from R to R and integrability for continuous functions. Formalized Mathematics, 9(2):281-284, 2001. | - |
| dc.description.references | Noboru Endou, Yasunari Shidama, and Keiichi Miyajima. Partial differentiation on normed linear spaces Rn. Formalized Mathematics, 15(2):65-72, 2007. doi:10.2478/v10037-007-0008-5. | - |
| dc.description.references | Hiroshi Imura, Morishige Kimura, and Yasunari Shidama. The differentiable functions on normed linear spaces. Formalized Mathematics, 12(3):321-327, 2004. | - |
| dc.description.references | Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5): 841-845, 1990. | - |
| dc.description.references | Eugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990. | - |
| dc.description.references | Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990. | - |
| dc.description.references | Keiichi Miyajima, Takahiro Kato, and Yasunari Shidama. Riemann integral of functions from R into real normed space. Formalized Mathematics, 19(1):17-22, 2011. doi:10.2478/v10037-011-0003-8. | - |
| dc.description.references | Keiichi Miyajima, Artur Korniłowicz, and Yasunari Shidama. Contracting mapping on normed linear space. Formalized Mathematics, 20(4):291-301, 2012. doi:10.2478/v10037-012-0035-8. | - |
| dc.description.references | Keiko Narita, Artur Korniłowicz, and Yasunari Shidama. The differentiable functions from R into Rn. Formalized Mathematics, 20(1):65-71, 2012. doi:10.2478/v10037-012-0009-x. | - |
| dc.description.references | Keiko Narita, Noboru Endou, and Yasunari Shidama. The linearity of Riemann integral on functions from R into real Banach space. Formalized Mathematics, 21(3):185-191, 2013. doi:10.2478/forma-2013-0020. | - |
| dc.description.references | Takaya Nishiyama, Artur Korniłowicz, and Yasunari Shidama. The uniform continuity of functions on normed linear spaces. Formalized Mathematics, 12(3):277-279, 2004. | - |
| dc.description.references | Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004. | - |
| dc.description.references | Hiroyuki Okazaki, Noboru Endou, Keiko Narita, and Yasunari Shidama. Differentiable functions into real normed spaces. Formalized Mathematics, 19(2):69-72, 2011. doi:10.2478/v10037-011-0012-7. | - |
| dc.description.references | Hiroyuki Okazaki, Noboru Endou, and Yasunari Shidama. More on continuous functions on normed linear spaces. Formalized Mathematics, 19(1):45-49, 2011. doi:10.2478/v10037-011-0008-3. | - |
| dc.description.references | Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991. | - |
| dc.description.references | Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990. | - |
| dc.description.references | Piotr Rudnicki and Andrzej Trybulec. Abian’s fixed point theorem. Formalized Mathematics, 6(3):335-338, 1997. | - |
| dc.description.references | Laurent Schwartz. Cours d’analyse, vol. 1. Hermann Paris, 1967. http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000271006300001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=b7bc2757938ac7a7a821505f8243d9f3 | - |
| dc.description.references | Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004. | - |
| 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. | - |
| dc.description.references | Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003. | - |
| dc.description.references | Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990. | - |
| dc.description.references | Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990. | - |
| dc.description.references | Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. | - |
| dc.description.references | Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990. | - |
| dc.description.references | Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. | - |
| Występuje w kolekcji(ach): | Formalized Mathematics, 2013, Volume 21, Issue 4 | |
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|---|---|---|---|---|
| forma-2013-0028.pdf | 279,91 kB | Adobe PDF | Otwórz |
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