-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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Mazaheri, H., Kazemi, R. (2007)
Novi Sad Journal of Mathematics
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Abbassi, Hossein, Nourouzi, Kourosh (2009)
International Journal of Open Problems in Computer Science and Mathematics. IJOPCM
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Gozali, S.M., Gunawan, H., Neswan, O. (2010)
Annals of Functional Analysis (AFA) [electronic only]
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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].
Chmieliński, Jacek (2007)
Banach Journal of Mathematical Analysis [electronic only]
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Noboru Endou, Yasunari Shidama (2013)
Formalized Mathematics
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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].
Goleţ, Ioan (2006)
Acta Universitatis Apulensis. Mathematics - Informatics
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Raja, P., Vaezpour, S.M. (2008)
The Journal of Nonlinear Sciences and its Applications
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Priya Raphael, Shaini Pulickakunnel (2012)
Kragujevac Journal of Mathematics
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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...
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.
Tyas Rangga Kristiantoo, Raden Akbar Wibawa-Kusumah, Hendra Gunawan (2013)
Matematički Vesnik
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