-nsr lemma and quotient space in -normed space
P. Riyas, K. T. Ravindran (2011)
Matematički Vesnik
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P. Riyas, K. T. Ravindran (2011)
Matematički Vesnik
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Goleţ, Ioan (2008)
Novi Sad Journal of Mathematics
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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].
Abbassi, Hossein, Nourouzi, Kourosh (2009)
International Journal of Open Problems in Computer Science and Mathematics. IJOPCM
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Mehmet Açikgöz (2009)
Matematički Vesnik
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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.
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.
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...
Gozali, S.M., Gunawan, H., Neswan, O. (2010)
Annals of Functional Analysis (AFA) [electronic only]
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Chmieliński, Jacek (2007)
Banach Journal of Mathematical Analysis [electronic only]
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Tyas Rangga Kristiantoo, Raden Akbar Wibawa-Kusumah, Hendra Gunawan (2013)
Matematički Vesnik
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Mazaheri, H., Kazemi, R. (2007)
Novi Sad Journal of Mathematics
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