Displaying similar documents to “Strongly ψ -bounded and classes of linear operators in probabilistic normed space.”

Contracting Mapping on Normed Linear Space

Keiichi Miyajima, Artur Korniłowicz, Yasunari Shidama (2012)

Formalized Mathematics

Similarity:

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].

Differentiable Functions on Normed Linear Spaces

Yasunari Shidama (2012)

Formalized Mathematics

Similarity:

In this article, we formalize differentiability of functions on normed linear spaces. Partial derivative, mean value theorem for vector-valued functions, continuous differentiability, etc. are formalized. As it is well known, there is no exact analog of the mean value theorem for vector-valued functions. However a certain type of generalization of the mean value theorem for vector-valued functions is obtained as follows: If ||ƒ'(x + t · h)|| is bounded for t between 0 and 1 by some constant...

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].