Some completeness theorems in the Menger probabilistic metric space.
Aghajani, Asadollah, Razani, Abdolrahman (2008)
APPS. Applied Sciences
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Aghajani, Asadollah, Razani, Abdolrahman (2008)
APPS. Applied Sciences
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Goleţ, Ioan (2006)
Acta Universitatis Apulensis. Mathematics - Informatics
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P. Riyas, K. T. Ravindran (2011)
Matematički Vesnik
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Rahmat, Mohamad Rafi Segi (2009)
International Journal of Open Problems in Computer Science and Mathematics. IJOPCM
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Abbassi, Hossein, Nourouzi, Kourosh (2009)
International Journal of Open Problems in Computer Science and Mathematics. IJOPCM
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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].
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.
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...
Tyas Rangga Kristiantoo, Raden Akbar Wibawa-Kusumah, Hendra Gunawan (2013)
Matematički Vesnik
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Priya Raphael, Shaini Pulickakunnel (2012)
Kragujevac Journal of Mathematics
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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].
Shakeri, S. (2008)
The Journal of Nonlinear Sciences and its Applications
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Chmieliński, Jacek (2007)
Banach Journal of Mathematical Analysis [electronic only]
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