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

Abstract

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

How to cite

top

Yuichi 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. [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  2. [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  3. [3] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990. 
  4. [4] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990. 
  5. [5] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  6. [6] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. 
  7. [7] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. 
  8. [8] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990. 
  9. [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. [10] Hiroshi Imura, Morishige Kimura, and Yasunari Shidama. The differentiable functions on normed linear spaces. Formalized Mathematics, 12(3):321-327, 2004. 
  11. [11] Hiroshi Imura, Yuji Sakai, and Yasunari Shidama. Differentiable functions on normed linear spaces. Part II. Formalized Mathematics, 12(3):371-374, 2004. 
  12. [12] Jarosław Kotowicz. Partial functions from a domain to a domain. Formalized Mathematics, 1(4):697-702, 1990. 
  13. [13] Eugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990. 
  14. [14] Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004. 
  15. [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. [16] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991. 
  17. [17] Laurent Schwartz. Cours d’analyse. Hermann, 1981.[WoS] 
  18. [18] Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004. 
  19. [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. [20] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990. 
  21. [21] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990. 
  22. [22] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  23. [23] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990. 
  24. [24] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 
  25. [25] Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992. 

NotesEmbed ?

top

You must be logged in to post comments.