An analogue of the Krein-Milman theorem for star-shaped sets.
Martini, Horst, Wenzel, Walter (2003)
Beiträge zur Algebra und Geometrie
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Martini, Horst, Wenzel, Walter (2003)
Beiträge zur Algebra und Geometrie
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Jolanta Plewnia (1993)
Annales Polonici Mathematici
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If C is a non-empty convex subset of a real linear space E, p: E → ℝ is a sublinear function and f:C → ℝ is concave and such that f ≤ p on C, then there exists a linear function g:E → ℝ such that g ≤ p on E and f ≤ g on C. In this result of Hirano, Komiya and Takahashi we replace the sublinearity of p by convexity.
Blezu, Dorin (2001)
General Mathematics
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Nikodem, Kazimierz, Páles, Zsolt (2011)
Banach Journal of Mathematical Analysis [electronic only]
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Sehie Park, Jong Park (1996)
Colloquium Mathematicae
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E. Ignaczak, A. Paszkiewicz (1998)
Applicationes Mathematicae
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We prove that under some topological assumptions (e.g. if M has nonempty interior in X), a convex cone M in a linear topological space X is a linear subspace if and only if each convex functional on M has a convex extension on the whole space X.
Acu, Mugur (2006)
Acta Universitatis Apulensis. Mathematics - Informatics
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Borwein, Jonathan, Lucet, Yves, Mordukhovich, Boris (2000)
Journal of Convex Analysis
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M. Beltagy (1993)
Commentationes Mathematicae Universitatis Carolinae
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In this paper, local, global, strongly local and strongly global supportings of subsets in a complete simply connected smooth Riemannian manifold without focal points are defined. Sufficient conditions for convexity of subsets in the same sort of manifolds have been derived in terms of the above mentioned types of supportings.
Foertsch, Thomas (2004)
Beiträge zur Algebra und Geometrie
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