Compactly epi-Lipschitzian convex sets and functions in normed spaces.
Borwein, Jonathan, Lucet, Yves, Mordukhovich, Boris (2000)
Journal of Convex Analysis
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Borwein, Jonathan, Lucet, Yves, Mordukhovich, Boris (2000)
Journal of Convex Analysis
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Suo, Hongmin (2009)
The Journal of Nonlinear Sciences and its Applications
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Bauschke, Heinz H., Borwein, Jonathan M., Tseng, Paul (2000)
Journal of Convex Analysis
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Pradipta Bandyopadhyaya (1992)
Colloquium Mathematicae
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Janusz Krzyszkowski (1995)
Annales Polonici Mathematici
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We give some necessary and sufficient conditions for an n-1 times differentiable function to be a generalized convex function with respect to an unrestricted n-parameter family.
Huynh Ngai, Michel Théra (2007)
Control and Cybernetics
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Siegfried Momm (1996)
Annales Polonici Mathematici
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A certain linear growth of the pluricomplex Green function of a bounded convex domain of at a given boundary point is related to the existence of a certain plurisubharmonic function called a “plurisubharmonic saddle”. In view of classical results on the existence of angular derivatives of conformal mappings, for the case of a single complex variable, this allows us to deduce a criterion for the existence of subharmonic saddles.
Slavov, Zdravko Dimitrov (2008)
Acta Universitatis Apulensis. Mathematics - Informatics
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Liangpeng Xiong, Xiaoli Liu (2012)
Kragujevac Journal of Mathematics
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Penot, Jean-Paul, Zălinescu, Constantin (2000)
Journal of Convex Analysis
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Janusz Matkowski, Marek Pycia (1995)
Annales Polonici Mathematici
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Let a and b be fixed real numbers such that 0 < mina,b < 1 < a + b. We prove that every function f:(0,∞) → ℝ satisfying f(as + bt) ≤ af(s) + bf(t), s,t > 0, and such that must be of the form f(t) = f(1)t, t > 0. This improves an earlier result in [5] where, in particular, f is assumed to be nonnegative. Some generalizations for functions defined on cones in linear spaces are given. We apply these results to give a new characterization of the -norm.
Chabi, El Hassan, Zouaki, Hamid (2000)
Journal of Convex Analysis
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Cârjă, Ovidiu, Monteiro Marques, Manuel D.P. (2000)
Journal of Convex Analysis
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