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2007 | 15 | 2 | 65-72
Tytuł artykułu

Partial Differentiation on Normed Linear Spaces R n

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Summary. In this article, we define the partial differentiation of functions of real variable and prove the linearity of this operator [18].
Słowa kluczowe
Wydawca
Rocznik
Tom
15
Numer
2
Strony
65-72
Opis fizyczny
Daty
wydano
2007-01-01
online
2008-06-09
Twórcy
autor
  • Gifu National College of Technology, Japan
  • Shinshu University, Nagano, Japan
  • Ibaraki University, Hitachi, Japan
Bibliografia
  • [12] Hiroshi Imura, Morishige Kimura, and Yasunari Shidama. The differentiable functions on normed linear spaces. Formalized Mathematics, 12(3):321-327, 2004.
  • [13] Jarosław Kotowicz. Partial functions from a domain to a domain. Formalized Mathematics, 1(4):697-702, 1990.
  • [14] Jarosław Kotowicz. Real sequences and basic operations on them. Formalized Mathematics, 1(2):269-272, 1990.
  • [15] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
  • [16] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.
  • [17] Konrad Raczkowski and Paweł Sadowski. Real function differentiability. Formalized Mathematics, 1(4):797-801, 1990.
  • [18] Laurent Schwartz. Cours d'analyse. Hermann, 1981.[WoS]
  • [19] Yasunari Shidama. Banach space of bounded linear operators. Formalized Mathematics, 12(1):39-48, 2004.
  • [20] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.
  • [21] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.
  • [22] Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.
  • [23] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  • [24] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [25] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  • [26] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
  • [27] Hiroshi Yamazaki, Yoshinori Fujisawa, and Yatsuka Nakamura. On replace function and swap function for finite sequences. Formalized Mathematics, 9(3):471-474, 2001.
  • [28] Hiroshi Yamazaki and Yasunari Shidama. Algebra of vector functions. Formalized Mathematics, 3(2):171-175, 1992.
  • [6] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [7] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [8] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.
  • [9] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
  • [10] Noboru Endou and Yasunari Shidama. Completeness of the real Euclidean space. Formalized Mathematics, 13(4):577-580, 2005.
  • [11] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
  • [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 Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
  • [4] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
  • [5] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-007-0008-5
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