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

The Differentiable Functions from R into R n

Keiko Narita, Artur Korniłowicz, Yasunari Shidama (2012)

Formalized Mathematics

Similarity:

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.

Differential Equations on Functions from R into Real Banach Space

Keiko Narita, Noboru Endou, Yasunari Shidama (2013)

Formalized Mathematics

Similarity:

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 C k Space

Katuhiko Kanazashi, Hiroyuki Okazaki, Yasunari Shidama (2013)

Formalized Mathematics

Similarity:

In this article, we formalize continuous differentiability of realvalued functions on n-dimensional real normed linear spaces. Next, we give a definition of the Ck space according to [23].

Differentiation in Normed Spaces

Noboru Endou, Yasunari Shidama (2013)

Formalized Mathematics

Similarity:

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].