On the p-drop theorem, 1 ≤ p ≤∞.
Abdelhakim Maaden (2002)
Extracta Mathematicae
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Displaying similar documents to “C-nearest points and the drop property.”
On the p-drop theorem, 1 ≤ p ≤∞.
Some properties on the closed subsets in Banach spaces
Abdelhakim Maaden, Abdelkader Stouti (2006)
Archivum Mathematicum
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It is shown that under natural assumptions, there exists a linear functional does not have supremum on a closed bounded subset. That is the James Theorem for non-convex bodies. Also, a non-linear version of the Bishop-Phelps Theorem and a geometrical version of the formula of the subdifferential of the sum of two functions are obtained.
Uniformly convex and uniformly smooth convex functions
Dominique Azé, Jean-Paul Penot (1995)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Antiproximinal ѕets in Banach ѕpaces
S. Cobzaş (1999)
Acta Universitatis Carolinae. Mathematica et Physica
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Some remarks on nonlinear functionals
Josef Kolomý (1970)
Commentationes Mathematicae Universitatis Carolinae
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Differentiability of convex functions on a Banach space with smooth bump function.
Li, Yongxin, Shi, Shuzhong (1994)
Journal of Convex Analysis
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Quotients of Continuous Convex Functions on Nonreflexive Banach Spaces
P. Holický, O. F. K. Kalenda, L. Veselý, L. Zajíček (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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On each nonreflexive Banach space X there exists a positive continuous convex function f such that 1/f is not a d.c. function (i.e., a difference of two continuous convex functions). This result together with known ones implies that X is reflexive if and only if each everywhere defined quotient of two continuous convex functions is a d.c. function. Our construction also gives a stronger version of Klee's result concerning renormings of nonreflexive spaces and non-norm-attaining functionals. ...