On generalized probabilistic 2-normed spaces.
Goleţ, Ioan (2006)
Acta Universitatis Apulensis. Mathematics - Informatics
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Goleţ, Ioan (2006)
Acta Universitatis Apulensis. Mathematics - Informatics
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Katuhiko Kanazashi, Hiroyuki Okazaki, Yasunari Shidama (2011)
Formalized Mathematics
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In this article, we describe some basic properties of the Banach algebra which is constructed from all bounded complex-valued functionals.
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.
P. Riyas, K. T. Ravindran (2011)
Matematički Vesnik
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Keiko Narita, Noboru Endou, Yasunari Shidama (2014)
Formalized Mathematics
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In this article, we deal with dual spaces and the Hahn-Banach Theorem. At the first, we defined dual spaces of real linear spaces and proved related basic properties. Next, we defined dual spaces of real normed spaces. We formed the definitions based on dual spaces of real linear spaces. In addition, we proved properties of the norm about elements of dual spaces. For the proof we referred to descriptions in the article [21]. Finally, applying theorems of the second section, we proved...
Mehmet Açikgöz (2009)
Matematički Vesnik
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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].
Yasunari Shidama, Hikofumi Suzuki, Noboru Endou (2008)
Formalized Mathematics
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In this article, we describe some basic properties of the Banach algebra which is constructed from all bounded functionals.MML identifier: C0SP1, version: 7.8.10 4.99.1005
Yuichi Futa, Noboru Endou, Yasunari Shidama (2013)
Formalized Mathematics
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In this article, we formalize isometric differentiable functions on real normed space [17], and their properties.