Isometric Differentiable Functions on Real Normed Space
Yuichi Futa; Noboru Endou; Yasunari Shidama
Formalized Mathematics (2013)
- Volume: 21, Issue: 4, page 249-260
- ISSN: 1426-2630
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topYuichi Futa, Noboru Endou, and Yasunari Shidama. "Isometric Differentiable Functions on Real Normed Space." Formalized Mathematics 21.4 (2013): 249-260. <http://eudml.org/doc/266600>.
@article{YuichiFuta2013,
abstract = {In this article, we formalize isometric differentiable functions on real normed space [17], and their properties.},
author = {Yuichi Futa, Noboru Endou, Yasunari Shidama},
journal = {Formalized Mathematics},
keywords = {isometric differentiable function},
language = {eng},
number = {4},
pages = {249-260},
title = {Isometric Differentiable Functions on Real Normed Space},
url = {http://eudml.org/doc/266600},
volume = {21},
year = {2013},
}
TY - JOUR
AU - Yuichi Futa
AU - Noboru Endou
AU - Yasunari Shidama
TI - Isometric Differentiable Functions on Real Normed Space
JO - Formalized Mathematics
PY - 2013
VL - 21
IS - 4
SP - 249
EP - 260
AB - In this article, we formalize isometric differentiable functions on real normed space [17], and their properties.
LA - eng
KW - isometric differentiable function
UR - http://eudml.org/doc/266600
ER -
References
top- [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] Zbl1276.46015
- [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] Zbl1276.26036
- [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.
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