## Second-Order Partial Differentiation of Real Ternary Functions

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).

Show Summary Details# Second-Order Partial Differentiation of Real Ternary Functions

#### Open Access

## Second-Order Partial Differentiation of Real Ternary Functions

## About the article

More options …# Formalized Mathematics

### (a computer assisted approach)

More options …

Editor-in-Chief: Matuszewski, Roman

4 Issues per year

SCImago Journal Rank (SJR) 2016: 0.207

Source Normalized Impact per Paper (SNIP) 2016: 0.315

Takao Inoué

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).

[1] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences.

*Formalized Mathematics*, 1(**1**):107-114, 1990.Google Scholar[2] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets.

*Formalized Mathematics*, 1(**3**):529-536, 1990.Google Scholar[3] Czesław Byliński. Functions and their basic properties.

*Formalized Mathematics*, 1(**1**):55-65, 1990.Google Scholar[4] Czesław Byliński. Functions from a set to a set.

*Formalized Mathematics*, 1(**1**):153-164, 1990.Google Scholar[5] Czesław Byliński. Partial functions.

*Formalized Mathematics*, 1(**2**):357-367, 1990.Google Scholar[6] Agata Darmochwał. The Euclidean space.

*Formalized Mathematics*, 2(**4**):599-603, 1991.Google Scholar[7] Noboru Endou, Yasunari Shidama, and Keiichi Miyajima. Partial differentiation on normed linear spaces R

^{n}.*Formalized Mathematics*, 15(**2**):65-72, 2007, doi:10.2478/v10037-007-0008-5.CrossrefGoogle Scholar[8] Krzysztof Hryniewiecki. Basic properties of real numbers.

*Formalized Mathematics*, 1(**1**):35-40, 1990.Google Scholar[9] Jarosław Kotowicz. Convergent sequences and the limit of sequences.

*Formalized Mathematics*, 1(**2**):273-275, 1990.Google Scholar[10] Jarosław Kotowicz. Real sequences and basic operations on them.

*Formalized Mathematics*, 1(**2**):269-272, 1990.Google Scholar[11] Konrad Raczkowski and Paweł Sadowski. Real function continuity.

*Formalized Mathematics*, 1(**4**):787-791, 1990.Google Scholar[12] Konrad Raczkowski and Paweł Sadowski. Real function differentiability.

*Formalized Mathematics*, 1(**4**):797-801, 1990.Google Scholar[13] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers.

*Formalized Mathematics*, 1(**4**):777-780, 1990.Google Scholar[14] Walter Rudin.

*Principles of Mathematical Analysis*. MacGraw-Hill, 1976.Google Scholar[15] Edmund Woronowicz. Relations defined on sets.

*Formalized Mathematics*, 1(**1**):181-186, 1990.Google Scholar[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.CrossrefGoogle Scholar[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.CrossrefGoogle Scholar

**Published Online**: 2011-01-05

**Published in Print**: 2010-01-01

**Citation Information: **Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-010-0015-9.

This content is open access.

## Comments (0)