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

Takao Inoué; Adam Naumowicz; Noboru Endou; Yasunari Shidama

Displaying similar documents to “ Partial Differentiation of Vector-Valued Functions on n -Dimensional Real Normed Linear Spaces ”

Differential Equations on Functions from R into Real Banach Space

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In this article, we describe the differential equations on functions from R into real Banach space. The descriptions are based on the article [20]. As preliminary to the proof of these theorems, we proved some properties of differentiable functions on real normed space. For the proof we referred to descriptions and theorems in the article [21] and the article [32]. And applying the theorems of Riemann integral introduced in the article [22], we proved the ordinary differential equations...

The Differentiable Functions from R into R n

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In control engineering, differentiable partial functions from R into Rn play a very important role. In this article, we formalized basic properties of such functions.

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

Takao Inoué, Noboru Endou, Yasunari Shidama (2010)

Formalized Mathematics

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In this article, we define and develop differentiation of vector-valued functions on n-dimensional real normed linear spaces (refer to [16] and [17]).

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Partial Differentiation, Differentiation and Continuity on n -Dimensional Real Normed Linear Spaces

Takao Inoué, Adam Naumowicz, Noboru Endou, Yasunari Shidama (2011)

Formalized Mathematics

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In this article, we aim to prove the characterization of differentiation by means of partial differentiation for vector-valued functions on n-dimensional real normed linear spaces (refer to [15] and [16]).

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Commentationes Mathematicae Universitatis Carolinae

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This paper gives a partial solution to a problem of W. Taylor on characterization of the unit interval in the class of all topological spaces by means of the first order properties of their clones. A characterization within the class of compact spaces is obtained.