Isometric Differentiable Functions on Real Normed Space
Yuichi Futa ; Noboru Endou ; Yasunari Shidama
Formalized Mathematics, Tome 21 (2013), p. 249-260 / Harvested from The Polish Digital Mathematics Library

In this article, we formalize isometric differentiable functions on real normed space [17], and their properties.

Publié le : 2013-01-01
EUDML-ID : urn:eudml:doc:266600
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     author = {Yuichi Futa and Noboru Endou and Yasunari Shidama},
     title = {Isometric Differentiable Functions on Real Normed Space},
     journal = {Formalized Mathematics},
     volume = {21},
     year = {2013},
     pages = {249-260},
     zbl = {1298.58010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0027}
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Yuichi Futa; Noboru Endou; Yasunari Shidama. Isometric Differentiable Functions on Real Normed Space. Formalized Mathematics, Tome 21 (2013) pp. 249-260. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_forma-2013-0027/

[1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

[2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.

[3] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.

[4] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.

[5] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.

[6] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.

[7] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.

[8] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.

[9] Noboru Endou, Yasunari Shidama, and Keiichi Miyajima. The product space of real normed spaces and its properties. Formalized Mathematics, 15(3):81-85, 2007. doi:10.2478/v10037-007-0010-y.[Crossref]

[10] Hiroshi Imura, Morishige Kimura, and Yasunari Shidama. The differentiable functions on normed linear spaces. Formalized Mathematics, 12(3):321-327, 2004.

[11] Hiroshi Imura, Yuji Sakai, and Yasunari Shidama. Differentiable functions on normed linear spaces. Part II. Formalized Mathematics, 12(3):371-374, 2004.

[12] Jarosław Kotowicz. Partial functions from a domain to a domain. Formalized Mathematics, 1(4):697-702, 1990.

[13] Eugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.

[14] Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004.

[15] 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.[Crossref] | Zbl 1276.46015

[16] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.

[17] Laurent Schwartz. Cours d’analyse. Hermann, 1981.[WoS]

[18] Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.

[19] Yasunari Shidama. Differentiable functions on normed linear spaces. Formalized Mathematics, 20(1):31-40, 2012. doi:10.2478/v10037-012-0005-1.[Crossref] | Zbl 1276.26036

[20] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.

[21] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.

[22] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

[23] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.

[24] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

[25] Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992.