The Linearity of Riemann Integral on Functions from ℝ into Real Banach Space

Keiko Narita; Noboru Endou; Yasunari Shidama

Displaying similar documents to “The Linearity of Riemann Integral on Functions from ℝ into Real Banach Space”

Riemann Integral of Functions from R into n -dimensional Real Normed Space

Keiichi Miyajima, Artur Korniłowicz, Yasunari Shidama (2012)

Formalized Mathematics

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In this article, we define the Riemann integral on functions R into n-dimensional real normed space and prove the linearity of this operator. As a result, the Riemann integration can be applied to the wider range. Our method refers to the [21].

Differential Equations on Functions from R into Real Banach Space

Keiko Narita, Noboru Endou, Yasunari Shidama (2013)

Formalized Mathematics

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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...

Partial Differentiation of Vector-Valued Functions 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 define and develop partial differentiation of vector-valued functions on n-dimensional real normed linear spaces (refer to [19] and [20]).

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The Differentiable Functions from R into R n

Keiko Narita, Artur Korniłowicz, Yasunari Shidama (2012)

Formalized Mathematics

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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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