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...

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.