Partial Differentiation of Real Ternary Functions

Takao Inoué; Bing Xie; Xiquan Liang

Formalized Mathematics (2010)

  • Volume: 18, Issue: 1, page 39-46
  • ISSN: 1426-2630

Abstract

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In this article, we shall extend the result of [19] to discuss partial differentiation of real ternary functions (refer to [8] and [16] for partial differentiation).

How to cite

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Takao Inoué, Bing Xie, and Xiquan Liang. "Partial Differentiation of Real Ternary Functions." Formalized Mathematics 18.1 (2010): 39-46. <http://eudml.org/doc/266775>.

@article{TakaoInoué2010,
abstract = {In this article, we shall extend the result of [19] to discuss partial differentiation of real ternary functions (refer to [8] and [16] for partial differentiation).},
author = {Takao Inoué, Bing Xie, Xiquan Liang},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {39-46},
title = {Partial Differentiation of Real Ternary Functions},
url = {http://eudml.org/doc/266775},
volume = {18},
year = {2010},
}

TY - JOUR
AU - Takao Inoué
AU - Bing Xie
AU - Xiquan Liang
TI - Partial Differentiation of Real Ternary Functions
JO - Formalized Mathematics
PY - 2010
VL - 18
IS - 1
SP - 39
EP - 46
AB - In this article, we shall extend the result of [19] to discuss partial differentiation of real ternary functions (refer to [8] and [16] for partial differentiation).
LA - eng
UR - http://eudml.org/doc/266775
ER -

References

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  1. [1] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990. 
  2. [2] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990. 
  3. [3] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990. 
  4. [4] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990. 
  5. [5] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990. 
  6. [6] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990. 
  7. [7] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991. 
  8. [8] 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.[Crossref] 
  9. [9] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990. 
  10. [10] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990. 
  11. [11] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990. 
  12. [12] Xiquan Liang, Piqing Zhao, and Ou Bai. Vector functions and their differentiation formulas in 3-dimensional Euclidean spaces. Formalized Mathematics, 18(1):1-10, 2010, doi: 10.2478/v10037-010-0001-2.[Crossref] 
  13. [13] Konrad Raczkowski and Paweł Sadowski. Real function continuity. Formalized Mathematics, 1(4):787-791, 1990. 
  14. [14] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990. 
  15. [15] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990. 
  16. [16] Walter Rudin. Principles of Mathematical Analysis. MacGraw-Hill, 1976. 
  17. [17] Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990. 
  18. [18] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 
  19. [19] Bing Xie, Xiquan Liang, and Hongwei Li. Partial differentiation of real binary functions. Formalized Mathematics, 16(4):333-338, 2008, doi:10.2478/v10037-008-0041-z.[Crossref] 

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