In this article, we formalize isometric differentiable functions on real normed space [17], and their properties.
@article{bwmeta1.element.doi-10_2478_forma-2013-0027, 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} }
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.