## Partial Differentiation on Normed Linear Spaces *R*^{n}

^{n}

Summary. In this article, we define the partial differentiation of functions of real variable and prove the linearity of this operator [18].

Show Summary Details# Partial Differentiation on Normed Linear Spaces *R*^{n}

#### Open Access

## Partial Differentiation on Normed Linear Spaces *R*^{n}

## About the article

## Citing Articles

*Formalized Mathematics*, 2012, Volume 20, Number 1*Formalized Mathematics*, 2011, Volume 19, Number 2*Formalized Mathematics*, 2011, Volume 19, Number 1, Page 1*Formalized Mathematics*, 2011, Volume 19, Number 4*Formalized Mathematics*, 2010, Volume 18, Number 2*Formalized Mathematics*, 2010, Volume 18, Number 1*Formalized Mathematics*, 2010, Volume 18, Number 4*Formalized Mathematics*, 2009, Volume 17, Number 2*Formalized Mathematics*, 2009, Volume 17, Number 2*Formalized Mathematics*, 2008, Volume 16, Number 4*Formalized Mathematics*, 2009, Volume 17, Number 2

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

Noboru Endou / Yasunari Shidama / Keiichi Miyajima

Summary. In this article, we define the partial differentiation of functions of real variable and prove the linearity of this operator [18].

[12] Hiroshi Imura, Morishige Kimura, and Yasunari Shidama. The differentiable functions on normed linear spaces.

*Formalized Mathematics*, 12(3):321-327, 2004.Google Scholar[13] Jarosław Kotowicz. Partial functions from a domain to a domain.

*Formalized Mathematics*, 1(4):697-702, 1990.Google Scholar[14] Jarosław Kotowicz. Real sequences and basic operations on them.

*Formalized Mathematics*, 1(2):269-272, 1990.Google Scholar[15] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions.

*Formalized Mathematics*, 1(1):223-230, 1990.Google Scholar[16] Jan Popiołek. Real normed space.

*Formalized Mathematics*, 2(1):111-115, 1991.Google Scholar[17] Konrad Raczkowski and Paweł Sadowski. Real function differentiability.

*Formalized Mathematics*, 1(4):797-801, 1990.Google Scholar[18] Laurent Schwartz.

*Cours d'analyse.*Hermann, 1981.Web of ScienceGoogle Scholar[19] Yasunari Shidama. Banach space of bounded linear operators.

*Formalized Mathematics*, 12(1):39-48, 2004.Google Scholar[20] Andrzej Trybulec. Subsets of complex numbers.

*To appear in Formalized Mathematics.*Google Scholar[21] Andrzej Trybulec. Tarski Grothendieck set theory.

*Formalized Mathematics*, 1(1):9-11, 1990.Google Scholar[22] Wojciech A. Trybulec. Pigeon hole principle.

*Formalized Mathematics*, 1(3):575-579, 1990.Google Scholar[23] Wojciech A. Trybulec. Vectors in real linear space.

*Formalized Mathematics*, 1(2):291-296, 1990.Google Scholar[24] Zinaida Trybulec. Properties of subsets.

*Formalized Mathematics*, 1(1):67-71, 1990.Google Scholar[25] Edmund Woronowicz. Relations and their basic properties.

*Formalized Mathematics*, 1(1):73-83, 1990.Google Scholar[26] Edmund Woronowicz. Relations defined on sets.

*Formalized Mathematics*, 1(1):181-186, 1990.Google Scholar[27] Hiroshi Yamazaki, Yoshinori Fujisawa, and Yatsuka Nakamura. On replace function and swap function for finite sequences.

*Formalized Mathematics*, 9(3):471-474, 2001.Google Scholar[28] Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions.

*Formalized Mathematics*, 3(2):171-175, 1992.Google Scholar[6] Czesław Byliński. Functions from a set to a set.

*Formalized Mathematics*, 1(1):153-164, 1990.Google Scholar[7] Czesław Byliński. Partial functions.

*Formalized Mathematics*, 1(2):357-367, 1990.Google Scholar[8] Czesław Byliński. The sum and product of finite sequences of real numbers.

*Formalized Mathematics*, 1(4):661-668, 1990.Google Scholar[9] Agata Darmochwał. The Euclidean space.

*Formalized Mathematics*, 2(4):599-603, 1991.Google Scholar[10] Noboru Endou and Yasunari Shidama. Completeness of the real Euclidean space.

*Formalized Mathematics*, 13(4):577-580, 2005.Google Scholar[11] Krzysztof Hryniewiecki. Basic properties of real numbers.

*Formalized Mathematics*, 1(1):35-40, 1990.Google Scholar[1] Grzegorz Bancerek. The ordinal numbers.

*Formalized Mathematics*, 1(1):91-96, 1990.Google Scholar[2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences.

*Formalized Mathematics*, 1(1):107-114, 1990.Google Scholar[3] Czesław Byliński. The complex numbers.

*Formalized Mathematics*, 1(3):507-513, 1990.Google Scholar[4] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets.

*Formalized Mathematics*, 1(3):529-536, 1990.Google Scholar[5] Czesław Byliński. Functions and their basic properties.

*Formalized Mathematics*, 1(1):55-65, 1990.Google Scholar

**Published Online**: 2008-06-09

**Published in Print**: 2007-01-01

**Citation Information: **Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-007-0008-5.

This content is open access.

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]

Keiko Narita, Artur Korniłowicz, and Yasunari Shidama

[2]

Takao Inoué, Adam Naumowicz, Noboru Endou, and Yasunari Shidama

[3]

Takao Inoué, Adam Naumowicz, Noboru Endou, and Yasunari Shidama

[4]

Keiko Narita, Artur Kornilowicz, and Yasunari Shidama

[5]

Takao Inoué

[6]

Takao Inoué, Bing Xie, and Xiquan Liang

[7]

Takao Inoué, Noboru Endou, and Yasunari Shidama

[8]

Keiichi Miyajima and Yasunari Shidama

[9]

Bing Xie, Xiquan Liang, and Xiuzhuan Shen

[10]

Bing Xie, Xiquan Liang, and Hongwei Li

[11]

Hiroshi Yamazaki, Yasunari Shidama, Yatsuka Nakamura, and Chanapat Pacharapokin

## Comments (0)