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2013 | 21 | 4 | 249-260
Tytuł artykułu

Isometric Differentiable Functions on Real Normed Space

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article, we formalize isometric differentiable functions on real normed space [17], and their properties.
Słowa kluczowe
Wydawca
Rocznik
Tom
21
Numer
4
Strony
249-260
Opis fizyczny
Daty
otrzymano
2013-12-31
Twórcy
autor
  • Japan Advanced Institute of Science and Technology Ishikawa, Japan
autor
  • Gifu National College of Technology Gifu, Japan
  • Shinshu University Nagano, Japan
Bibliografia
  • [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • [3] Czesław Bylinski. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
  • [4] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
  • [5] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [6] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [7] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [8] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
  • [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.[Crossref]
  • [10] Hiroshi Imura, Morishige Kimura, and Yasunari Shidama. The differentiable functions on normed linear spaces. Formalized Mathematics, 12(3):321-327, 2004.
  • [11] Hiroshi Imura, Yuji Sakai, and Yasunari Shidama. Differentiable functions on normed linear spaces. Part II. Formalized Mathematics, 12(3):371-374, 2004.
  • [12] Jarosław Kotowicz. Partial functions from a domain to a domain. Formalized Mathematics, 1(4):697-702, 1990.
  • [13] Eugeniusz Kusak, Wojciech Leonczuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
  • [14] Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004.
  • [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.[Crossref]
  • [16] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.
  • [17] Laurent Schwartz. Cours d’analyse. Hermann, 1981.[WoS]
  • [18] Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.
  • [19] Yasunari Shidama. Differentiable functions on normed linear spaces. Formalized Mathematics, 20(1):31-40, 2012. doi:10.2478/v10037-012-0005-1.[Crossref]
  • [20] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.
  • [21] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  • [22] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [23] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
  • [24] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
  • [25] Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_forma-2013-0027
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