Differentiable Functions into Real Normed Spaces
Hiroyuki Okazaki ; Noboru Endou ; Keiko Narita ; Yasunari Shidama
Formalized Mathematics, Tome 19 (2011), p. 69-72 / Harvested from The Polish Digital Mathematics Library

In this article, we formalize the differentiability of functions from the set of real numbers into a normed vector space [14].

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:266910
@article{bwmeta1.element.doi-10_2478_v10037-011-0012-7,
     author = {Hiroyuki Okazaki and Noboru Endou and Keiko Narita and Yasunari Shidama},
     title = {Differentiable Functions into Real Normed Spaces},
     journal = {Formalized Mathematics},
     volume = {19},
     year = {2011},
     pages = {69-72},
     zbl = {1276.26035},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-011-0012-7}
}
Hiroyuki Okazaki; Noboru Endou; Keiko Narita; Yasunari Shidama. Differentiable Functions into Real Normed Spaces. Formalized Mathematics, Tome 19 (2011) pp. 69-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-011-0012-7/

[1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

[2] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55- 65, 1990.

[3] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.

[4] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.

[5] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.

[6] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.

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

[8] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.

[9] Hiroyuki Okazaki, Noboru Endou, and Yasunari Shidama. More on continuous functions on normed linear spaces. Formalized Mathematics, 19(1):45-49, 2011, doi: 10.2478/v10037-011-0008-3.[Crossref] | Zbl 1276.46063

[10] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.

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

[12] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990.

[13] Konrad Raczkowski and Paweł Sadowski. Topological properties of subsets in real numbers. Formalized Mathematics, 1(4):777-780, 1990.

[14] Laurent Schwartz. Cours d'analyse, vol. 1. Hermann Paris, 1967.[WoS]

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

[16] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

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

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

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