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Formalized Mathematics

(a computer assisted approach)

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

Open Access
Online
ISSN
1898-9934
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Volume 21, Issue 4

Issues

Isometric Differentiable Functions on Real Normed Space

Yuichi Futa / Noboru Endou / Yasunari Shidama
Published Online: 2013-12-27 | DOI: https://doi.org/10.2478/forma-2013-0027

Abstract

In this article, we formalize isometric differentiable functions on real normed space [17], and their properties.

Keywords: isometric differentiable function

References

  • [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 Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.Google Scholar

  • [4] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.Google Scholar

  • [5] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.Google Scholar

  • [6] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.Google Scholar

  • [7] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.Google Scholar

  • [8] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.Google Scholar

  • [9] Noboru Endou, Yasunari Shidama, and Keiichi Miyajima. The product space of real normed spaces and its properties. Formalized Mathematics, 15(3):81-85, 2007. doi:10.2478/v10037-007-0010-y.CrossrefGoogle Scholar

  • [10] Hiroshi Imura, Morishige Kimura, and Yasunari Shidama. The differentiable functions on normed linear spaces. Formalized Mathematics, 12(3):321-327, 2004.Google Scholar

  • [11] Hiroshi Imura, Yuji Sakai, and Yasunari Shidama. Differentiable functions on normed linear spaces. Part II. Formalized Mathematics, 12(3):371-374, 2004.Google Scholar

  • [12] Jarosław Kotowicz. Partial functions from a domain to a domain. Formalized Mathematics, 1(4):697-702, 1990.Google Scholar

  • [13] Eugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.Google Scholar

  • [14] Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004.Google Scholar

  • [15] Hiroyuki Okazaki, Noboru Endou, and Yasunari Shidama. Cartesian products of family of real linear spaces. Formalized Mathematics, 19(1):51-59, 2011. doi:10.2478/v10037-011-0009-2.CrossrefGoogle Scholar

  • [16] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.Google Scholar

  • [17] Laurent Schwartz. Cours d’analyse. Hermann, 1981.Web of ScienceGoogle Scholar

  • [18] Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.Google Scholar

  • [19] Yasunari Shidama. Differentiable functions on normed linear spaces. Formalized Mathematics, 20(1):31-40, 2012. doi:10.2478/v10037-012-0005-1.CrossrefGoogle Scholar

  • [20] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.Google Scholar

  • [21] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990. Google Scholar

  • [22] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.Google Scholar

  • [23] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.Google Scholar

  • [24] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.Google Scholar

  • [25] Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992.Google Scholar

About the article

Received: 2013-12-31

Published Online: 2013-12-27

Published in Print: 2013-12-01


Citation Information: Formalized Mathematics, Volume 21, Issue 4, Pages 249–260, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/forma-2013-0027.

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© by Yuichi Futa. This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. (CC BY-SA 3.0) BY-SA 3.0

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