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Formalized Mathematics

(a computer assisted approach)

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Volume 19, Issue 1 (Jan 2011)

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

Takao Inoué
  • Inaba 2205, Wing-Minamikan Nagano, Nagano, Japan
/ Adam Naumowicz
  • Institute of Computer Science, University of Białystok, Akademicka 2, 15-267 Białystok, Poland
/ Noboru Endou
  • Gifu National College of Technology, Japan
/ Yasunari Shidama
  • Shinshu University, Nagano, Japan
Published Online: 2011-07-18 | DOI: https://doi.org/10.2478/v10037-011-0001-x

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

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]).

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

  • [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]

  • [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. [Web of Science]

  • [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.

About the article


Published Online: 2011-07-18

Published in Print: 2011-01-01



Citation Information: Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-011-0001-x. Export Citation

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[1]
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Formalized Mathematics, 2012, Volume 20, Number 1

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