Differentiable Functions into Real Normed Spaces

• Autorzy: Hiroyuki Okazaki , Noboru Endou , Keiko Narita , Yasunari Shidama
• Języki publikacji: EN

Abstrakty

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2011
• Tom: 19
• Numer: 2
• Strony: 69-72

Daty

wydano

2011-01-01

online

2011-07-18

Twórcy

autor

Hiroyuki Okazaki

• Shinshu University, Nagano, Japan

autor

Noboru Endou

• Nagano National College of Technology, Nagano, Japan

autor

Keiko Narita

• Hirosaki-city, Aomori, Japan

autor

Yasunari Shidama

• Shinshu University, Nagano, Japan

Bibliografia

• [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]
• [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.

Identyfikatory

DOI

10.2478/v10037-011-0012-7