Partial Differentiation of Vector-Valued Functions on n -Dimensional Real Normed Linear Spaces

Takao Inoué; Adam Naumowicz; Noboru Endou; Yasunari Shidama

Formalized Mathematics (2011)

  • Volume: 19, Issue: 1, page 1-9
  • ISSN: 1426-2630

Abstract

top
In this article, we define and develop partial differentiation of vector-valued functions on n-dimensional real normed linear spaces (refer to [19] and [20]).

How to cite

top

Takao Inoué, et al. " Partial Differentiation of Vector-Valued Functions on n -Dimensional Real Normed Linear Spaces ." Formalized Mathematics 19.1 (2011): 1-9. <http://eudml.org/doc/266848>.

@article{TakaoInoué2011,
abstract = {In this article, we define and develop partial differentiation of vector-valued functions on n-dimensional real normed linear spaces (refer to [19] and [20]).},
author = {Takao Inoué, Adam Naumowicz, Noboru Endou, Yasunari Shidama},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {1-9},
title = { Partial Differentiation of Vector-Valued Functions on n -Dimensional Real Normed Linear Spaces },
url = {http://eudml.org/doc/266848},
volume = {19},
year = {2011},
}

TY - JOUR
AU - Takao Inoué
AU - Adam Naumowicz
AU - Noboru Endou
AU - Yasunari Shidama
TI - Partial Differentiation of Vector-Valued Functions on n -Dimensional Real Normed Linear Spaces
JO - Formalized Mathematics
PY - 2011
VL - 19
IS - 1
SP - 1
EP - 9
AB - In this article, we define and develop partial differentiation of vector-valued functions on n-dimensional real normed linear spaces (refer to [19] and [20]).
LA - eng
UR - http://eudml.org/doc/266848
ER -

References

top
  1. [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. Zbl06213858
  2. [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  3. [3] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990. 
  4. [4] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  5. [5] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  6. [6] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. 
  7. [7] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991. 
  8. [8] Noboru Endou and Yasunari Shidama. Completeness of the real Euclidean space. Formalized Mathematics, 13(4):577-580, 2005. 
  9. [9] Noboru Endou, Yasunari Shidama, and Keiichi Miyajima. Partial differentiation on normed linear spaces n. Formalized Mathematics, 15(2):65-72, 2007, doi:10.2478/v10037-007-0008-5.[Crossref] 
  10. [10] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990. 
  11. [11] Hiroshi Imura, Morishige Kimura, and Yasunari Shidama. The differentiable functions on normed linear spaces. Formalized Mathematics, 12(3):321-327, 2004. 
  12. [12] Takao Inoué, Noboru Endou, and Yasunari Shidama. Differentiation of vector-valued functions on n-dimensional real normed linear spaces. Formalized Mathematics, 18(4):207-212, 2010, doi: 10.2478/v10037-010-0025-7.[Crossref] Zbl1276.26033
  13. [13] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990. 
  14. [14] Jarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275-278, 1992. 
  15. [15] Yatsuka Nakamura, Artur Korniłowicz, Nagato Oya, and Yasunari Shidama. The real vector spaces of finite sequences are finite dimensional. Formalized Mathematics, 17(1):1-9, 2009, doi:10.2478/v10037-009-0001-2.[Crossref] 
  16. [16] Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004. 
  17. [17] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990. 
  18. [18] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990. 
  19. [19] Walter Rudin. Principles of Mathematical Analysis. MacGraw-Hill, 1976. 
  20. [20] Laurent Schwartz. Cours d'analyse. Hermann, 1981.[WoS] 
  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 defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 
  24. [24] Hiroshi Yamazaki, Yoshinori Fujisawa, and Yatsuka Nakamura. On replace function and swap function for finite sequences. Formalized Mathematics, 9(3):471-474, 2001. 

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.