Partial Differentiation of Vector-Valued Functions on n -Dimensional Real Normed Linear Spaces

Takao Inoué ; Adam Naumowicz ; Noboru Endou ; Yasunari Shidama

Formalized Mathematics, Tome 19 (2011), p. 1-9 / Harvested from The Polish Digital Mathematics Library

Résumé

In this article, we define and develop partial differentiation of vector-valued functions on n-dimensional real normed linear spaces (refer to [19] and [20]).

Détail

Publié le : 2011-01-01

Zbl 1276.26033

EUDML-ID : urn:eudml:doc:266848

Bibliographie

[1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990. | Zbl 06213858

[2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.

[3] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.

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

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

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

[7] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.

[8] Noboru Endou and Yasunari Shidama. Completeness of the real Euclidean space. Formalized Mathematics, 13(4):577-580, 2005.

[9] Noboru Endou, Yasunari Shidama, and Keiichi Miyajima. Partial differentiation on normed linear spaces n. Formalized Mathematics, 15(2):65-72, 2007, doi:10.2478/v10037-007-0008-5.[Crossref]

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

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

[12] Takao Inoué, Noboru Endou, and Yasunari Shidama. Differentiation of vector-valued functions on n-dimensional real normed linear spaces. Formalized Mathematics, 18(4):207-212, 2010, doi: 10.2478/v10037-010-0025-7.[Crossref] | Zbl 1276.26033

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

[14] Jarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275-278, 1992.

[15] Yatsuka Nakamura, Artur Korniłowicz, Nagato Oya, and Yasunari Shidama. The real vector spaces of finite sequences are finite dimensional. Formalized Mathematics, 17(1):1-9, 2009, doi:10.2478/v10037-009-0001-2.[Crossref]

[16] Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004.

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

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

[19] Walter Rudin. Principles of Mathematical Analysis. MacGraw-Hill, 1976.

[20] Laurent Schwartz. Cours d'analyse. Hermann, 1981.[WoS]

[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 defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

[24] Hiroshi Yamazaki, Yoshinori Fujisawa, and Yatsuka Nakamura. On replace function and swap function for finite sequences. Formalized Mathematics, 9(3):471-474, 2001.