Differentiable Functions into Real Normed Spaces

Hiroyuki Okazaki; Noboru Endou; Keiko Narita; Yasunari Shidama

Formalized Mathematics (2011)

  • Volume: 19, Issue: 2, page 69-72
  • ISSN: 1426-2630

Abstract

top
In this article, we formalize the differentiability of functions from the set of real numbers into a normed vector space [14].

How to cite

top

Hiroyuki Okazaki, et al. "Differentiable Functions into Real Normed Spaces." Formalized Mathematics 19.2 (2011): 69-72. <http://eudml.org/doc/266910>.

@article{HiroyukiOkazaki2011,
abstract = {In this article, we formalize the differentiability of functions from the set of real numbers into a normed vector space [14].},
author = {Hiroyuki Okazaki, Noboru Endou, Keiko Narita, Yasunari Shidama},
journal = {Formalized Mathematics},
language = {eng},
number = {2},
pages = {69-72},
title = {Differentiable Functions into Real Normed Spaces},
url = {http://eudml.org/doc/266910},
volume = {19},
year = {2011},
}

TY - JOUR
AU - Hiroyuki Okazaki
AU - Noboru Endou
AU - Keiko Narita
AU - Yasunari Shidama
TI - Differentiable Functions into Real Normed Spaces
JO - Formalized Mathematics
PY - 2011
VL - 19
IS - 2
SP - 69
EP - 72
AB - In this article, we formalize the differentiability of functions from the set of real numbers into a normed vector space [14].
LA - eng
UR - http://eudml.org/doc/266910
ER -

References

top
  1. [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990. 
  2. [2] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55- 65, 1990. 
  3. [3] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  4. [4] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. 
  5. [5] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990. 
  6. [6] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990. 
  7. [7] Hiroshi Imura, Morishige Kimura, and Yasunari Shidama. The differentiable functions on normed linear spaces. Formalized Mathematics, 12(3):321-327, 2004. 
  8. [8] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990. 
  9. [9] 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.[Crossref] Zbl1276.46063
  10. [10] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990. 
  11. [11] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991. 
  12. [12] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990. 
  13. [13] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990. 
  14. [14] Laurent Schwartz. Cours d'analyse, vol. 1. Hermann Paris, 1967.[WoS] 
  15. [15] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990. 
  16. [16] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990. 
  17. [17] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990. 
  18. [18] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 
  19. [19] 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.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.