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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].
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...
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]).
Lyantse, W.E., Kudrik, T.S. (2002)
Sibirskij Matematicheskij Zhurnal
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Kudajbergenov, K.Zh. (2002)
Sibirskij Matematicheskij Zhurnal
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Kiyatkin, V.R. (2000)
Siberian Mathematical Journal
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Lewandowski, Arkadiusz (2008)
Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica
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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.
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]).
Korobkov, M.V. (2002)
Sibirskij Matematicheskij Zhurnal
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Korobkov, M.V. (2000)
Siberian Mathematical Journal
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