Czasopismo
Tytuł artykułu
Warianty tytułu
Języki publikacji
Abstrakty
In this article, we formalize continuous differentiability of realvalued functions on n-dimensional real normed linear spaces. Next, we give a definition of the Ck space according to [23].
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
25-31
Opis fizyczny
Daty
wydano
2013-01-01
Twórcy
autor
- Shizuoka City, Japan
autor
- Shinshu University Nagano, Japan
autor
- Shinshu University Nagano, Japan
Bibliografia
- [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
- [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
- [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
- [4] Czesław Bylinski. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
- [5] Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. FormalizedMathematics, 1(3):529-536, 1990.
- [6] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
- [7] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
- [8] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
- [9] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
- [10] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
- [11] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
- [12] Noboru Endou, Hiroyuki Okazaki, and Yasunari Shidama. Higher-order partial differentiation. Formalized Mathematics, 20(2):113-124, 2012. doi:10.2478/v10037-012-0015-z.[Crossref]
- [13] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1): 35-40, 1990.
- [14] Takao Inou´e, Adam Naumowicz, Noboru Endou, and Yasunari Shidama. Partial differentiation of vector-valued functions on n-dimensional real normed linear spaces. FormalizedMathematics, 19(1):1-9, 2011. doi:10.2478/v10037-011-0001-x.[Crossref]
- [15] Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5): 841-845, 1990.
- [16] Beata Perkowska. Functional sequence from a domain to a domain. Formalized Mathematics, 3(1):17-21, 1992.
- [17] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1 (2):329-334, 1990.
- [18] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4): 341-347, 2003.
- [19] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
- [20] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
- [21] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
- [22] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
- [23] Kosaku Yosida. Functional Analysis. Springer Classics in Mathematics, 1996.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_forma-2013-0002