Have a personal or library account? Click to login
Partial Differentiation of Vector-Valued Functions on n-Dimensional Real Normed Linear Spaces Cover

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

Formalized Mathematics
Volume 19 (2011): Issue 1 (March 2011)
By: Takao Inoué,  Adam Naumowicz,  Noboru Endou and  Yasunari Shidama  
Open Access
|Jul 2011

References

  1. [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
    Search in Google Scholar
  2. [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
    Search in Google Scholar
  3. [3] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
    Search in Google Scholar
  4. [4] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
    Search in Google Scholar
  5. [5] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
    Search in Google Scholar
  6. [6] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
    Search in Google Scholar
  7. [7] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
    Search in Google Scholar
  8. [8] Noboru Endou and Yasunari Shidama. Completeness of the real Euclidean space. Formalized Mathematics, 13(4):577-580, 2005.
    Search in Google Scholar
  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/v10037-007-0008-5.10.2478/v10037-007-0008-5
    Search in Google Scholar
  10. [10] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
    Search in Google Scholar
  11. [11] Hiroshi Imura, Morishige Kimura, and Yasunari Shidama. The differentiable functions on normed linear spaces. Formalized Mathematics, 12(3):321-327, 2004.
    Search in Google Scholar
  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/v10037-010-0025-7.10.2478/v10037-010-0025-7
    Search in Google Scholar
  13. [13] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
    Search in Google Scholar
  14. [14] Jarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275-278, 1992.
    Search in Google Scholar
  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/v10037-009-0001-2.10.2478/v10037-009-0001-2
    Search in Google Scholar
  16. [16] Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004.
    Search in Google Scholar
  17. [17] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
    Search in Google Scholar
  18. [18] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.
    Search in Google Scholar
  19. [19] Walter Rudin. Principles of Mathematical Analysis. MacGraw-Hill, 1976.
    Search in Google Scholar
  20. [20] Laurent Schwartz. Cours d'analyse. Hermann, 1981.
    Search in Google Scholar
  21. [21] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
    Search in Google Scholar
  22. [22] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
    Search in Google Scholar
  23. [23] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
    Search in Google Scholar
  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.
    Search in Google Scholar
DOI: https://doi.org/10.2478/v10037-011-0001-x | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Journal RSS Feed
Language: English
Page range: 1 - 9
Published on: Jul 18, 2011
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Related subjects:
Mathematics,
General mathematics,
Computer sciences,
Computer sciences, other

© 2011 Takao Inoué, Adam Naumowicz, Noboru Endou, Yasunari Shidama, published by University of Białystok
This work is licensed under the Creative Commons License.

Volume 19 (2011): Issue 1 (March 2011)