Displaying similar documents to “On generalized probabilistic 2-normed 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].

Functional Space C (ω), C 0 (ω)

Katuhiko Kanazashi, Hiroyuki Okazaki, Yasunari Shidama (2012)

Formalized Mathematics

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In this article, first we give a definition of a functional space which is constructed from all complex-valued continuous functions defined on a compact topological space. We prove that this functional space is a Banach algebra. Next, we give a definition of a function space which is constructed from all complex-valued continuous functions with bounded support. We also prove that this function space is a complex normed space.

Differentiable Functions on Normed Linear Spaces

Yasunari Shidama (2012)

Formalized Mathematics

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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...