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

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

Open Access
|Jan 2011

References

  1. [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 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 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] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  8. [8] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
  9. [9] Noboru Endou and Yasunari Shidama. Completeness of the real Euclidean space. Formalized Mathematics, 13(4):577-580, 2005.
  10. [10] Noboru Endou, Yasunari Shidama, and Keiichi Miyajima. Partial differentiation on normed linear spaces Rn. Formalized Mathematics, 15(2):65-72, 2007, doi:10.2478/v10037-007-0008-5.10.2478/v10037-007-0008-5
  11. [11] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
  12. [12] Hiroshi Imura, Morishige Kimura, and Yasunari Shidama. The differentiable functions on normed linear spaces. Formalized Mathematics, 12(3):321-327, 2004.
  13. [13] Keiichi Miyajima and Yasunari Shidama. Riemann integral of functions from R into Rn. Formalized Mathematics, 17(2):179-185, 2009, doi: 10.2478/v10037-009-0021-y.10.2478/v10037-009-0021-y
  14. [14] 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
  15. [15] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
  16. [16] Walter Rudin. Principles of Mathematical Analysis. MacGraw-Hill, 1976.
  17. [17] Laurent Schwartz. Cours d'analyse. Hermann, 1981.
  18. [18] Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.
  19. [19] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  20. [20] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  21. [21] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
DOI: https://doi.org/10.2478/v10037-010-0025-7 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 207 - 212
Published on: Jan 5, 2011
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

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

Volume 18 (2010): Issue 4 (December 2010)