On nicely smooth Banach spaces.
Pradipta Bandyopadhyay, Sudeshna Basu (2001)
Extracta Mathematicae
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Pradipta Bandyopadhyay, Sudeshna Basu (2001)
Extracta Mathematicae
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Abdelhakim Maaden (2001)
Extracta Mathematicae
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Tomás Domínguez Benavides (2002)
Extracta Mathematicae
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A. Aizpuru, F. J. García-Pacheco (2004)
Extracta Mathematicae
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Sven Bartels, Diethard Pallaschke (1994)
Applicationes Mathematicae
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Two properties concerning the space of differences of sublinear functions D(X) for a real Banach space X are proved. First, we show that for a real separable Banach space (X,‖·‖) there exists a countable family of seminorms such that D(X) becomes a Fréchet space. For X = ℝ^n this construction yields a norm such that D(ℝ^n) becomes a Banach space. Furthermore, we show that for a real Banach space with a smooth dual every sublinear Lipschitzian function can be expressed by the Fenchel...
M. Fabian, V. Zizler (2001)
Extracta Mathematicae
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J. Orihuela (2007)
Extracta Mathematicae
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Petr Hájek, Michal Johanis (2003)
Open Mathematics
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In any separable Banach space containing c 0 which admits a C k-smooth bump, every continuous function can be approximated by a C k-smooth function whose range of derivative is of the first category. Moreover, the approximation can be constructed in such a way that its derivative avoids a prescribed countable set (in particular the approximation can have no critical points). On the other hand, in a Banach space with the RNP, the range of the derivative of every smooth bounded bump contains...
Zarghami, R. (2010)
The Journal of Nonlinear Sciences and its Applications
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Pradipta Bandyopadhyaya (1992)
Colloquium Mathematicae
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