Second-Order Partial Differentiation of Real Ternary Functions

Takao Inoué

Formalized Mathematics (2010)

  • Volume: 18, Issue: 2, page 113-127
  • ISSN: 1426-2630

Abstract

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In this article, we shall extend the result of [17] to discuss second-order partial differentiation of real ternary functions (refer to [7] and [14] for partial differentiation).

How to cite

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Takao Inoué. "Second-Order Partial Differentiation of Real Ternary Functions." Formalized Mathematics 18.2 (2010): 113-127. <http://eudml.org/doc/266902>.

@article{TakaoInoué2010,
abstract = {In this article, we shall extend the result of [17] to discuss second-order partial differentiation of real ternary functions (refer to [7] and [14] for partial differentiation).},
author = {Takao Inoué},
journal = {Formalized Mathematics},
language = {eng},
number = {2},
pages = {113-127},
title = {Second-Order Partial Differentiation of Real Ternary Functions},
url = {http://eudml.org/doc/266902},
volume = {18},
year = {2010},
}

TY - JOUR
AU - Takao Inoué
TI - Second-Order Partial Differentiation of Real Ternary Functions
JO - Formalized Mathematics
PY - 2010
VL - 18
IS - 2
SP - 113
EP - 127
AB - In this article, we shall extend the result of [17] to discuss second-order partial differentiation of real ternary functions (refer to [7] and [14] for partial differentiation).
LA - eng
UR - http://eudml.org/doc/266902
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] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991. 
  7. [7] 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] 
  8. [8] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990. 
  9. [9] Jarosław Kotowicz. Convergent sequences and the limit of sequences. Formalized Mathematics, 1(2):273-275, 1990. 
  10. [10] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990. 
  11. [11] Konrad Raczkowski and Paweł Sadowski. Real function continuity. Formalized Mathematics, 1(4):787-791, 1990. 
  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] Walter Rudin. Principles of Mathematical Analysis. MacGraw-Hill, 1976. 
  15. [15] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990. 
  16. [16] 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] 
  17. [17] Bing Xie, Xiquan Liang, and Xiuzhuan Shen. Second-order partial differentiation of real binary functions. Formalized Mathematics, 17(2):79-87, 2009, doi: 10.2478/v10037-009-0009-7.[Crossref] 

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