Displaying similar documents to “Differentiable Functions on Normed Linear Spaces”

Contracting Mapping on Normed Linear Space

Keiichi Miyajima, Artur Korniłowicz, Yasunari Shidama (2012)

Formalized Mathematics

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In this article, we described the contracting mapping on normed linear space. Furthermore, we applied that mapping to ordinary differential equations on real normed space. Our method is based on the one presented by Schwarz [29].

Differentiation in Normed Spaces

Noboru Endou, Yasunari Shidama (2013)

Formalized Mathematics

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In this article we formalized the Fréchet differentiation. It is defined as a generalization of the differentiation of a real-valued function of a single real variable to more general functions whose domain and range are subsets of normed spaces [14].

Riemann Integral of Functions from ℝ into Real Banach Space

Keiko Narita, Noboru Endou, Yasunari Shidama (2013)

Formalized Mathematics

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In this article we deal with the Riemann integral of functions from R into a real Banach space. The last theorem establishes the integrability of continuous functions on the closed interval of reals. To prove the integrability we defined uniform continuity for functions from R into a real normed space, and proved related theorems. We also stated some properties of finite sequences of elements of a real normed space and finite sequences of real numbers. In addition we proved some theorems...

Differentiable Functions into Real Normed Spaces

Hiroyuki Okazaki, Noboru Endou, Keiko Narita, Yasunari Shidama (2011)

Formalized Mathematics

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In this article, we formalize the differentiability of functions from the set of real numbers into a normed vector space [14].

More on Continuous Functions on Normed Linear Spaces

Hiroyuki Okazaki, Noboru Endou, Yasunari Shidama (2011)

Formalized Mathematics

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In this article we formalize the definition and some facts about continuous functions from R into normed linear spaces [14].

More on the Continuity of Real Functions

Keiko Narita, Artur Kornilowicz, Yasunari Shidama (2011)

Formalized Mathematics

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In this article we demonstrate basic properties of the continuous functions from R to Rn which correspond to state space equations in control engineering.