Some properties of convex metric spaces
B. Krakus (1972)
Fundamenta Mathematicae
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Displaying similar documents to “A 'hidden' characterization of polyhedral convex sets”
Some properties of convex metric spaces
Strictly convex metric spaces with round balls and fixed points
Inese Bula (2005)
Banach Center Publications
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The paper introduces a notion of strictly convex metric space and strictly convex metric space with round balls. These objects generalize the well known concept of strictly convex Banach space. We prove some fixed point theorems in strictly convex metric spaces with round balls.
Some fixed point theorems in logarithmic convex structures
Alireza Moazzen, Yoel-Je Cho, Choonkil Park, Madjid Eshaghi Gordji (2017)
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On Convex Sets with Convex-Hereditary CEP
Tadeusz Dobrowolski (2011)
Bulletin of the Polish Academy of Sciences. Mathematics
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CEP stands for the compact extension property. We characterize nonlocally convex complete metric linear spaces with convex-hereditary CEP.
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Tulsi Dass Narang (1981)
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Selections and near-selections in metric linear spaces without local convexity
Tadeusz Dobrowolski, Jan van Mill (2006)
Fundamenta Mathematicae
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We characterize the AR property in convex subsets of metric linear spaces in terms of certain near-selections.
Paraconvex functions and paraconvex sets
Huynh Van Ngai, Jean-Paul Penot (2008)
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We study a class of functions which contains both convex functions and differentiable functions whose derivatives are locally Lipschitzian or Hölderian. This class is a subclass of the class of approximately convex functions. It enjoys refined properties. We also introduce a class of sets whose associated distance functions are of that type. We discuss the properties of the metric projections on such sets under some assumptions on the geometry of the Banach spaces in which they are embedded....
On convex metric spaces V
R. Duda (1970)
Fundamenta Mathematicae
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On order and metric convexities in
M. Changat, A. Vijayakumar (1992)
Compositio Mathematica
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The convexity of the subset space of a metric space
V. W. Bryant (1970)
Compositio Mathematica
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Continuous Selections in α-Convex Metric Spaces
F. S. De Blasi, G. Pianigiani (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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The existence of continuous selections is proved for a class of lower semicontinuous multifunctions whose values are closed convex subsets of a complete metric space equipped with an appropriate notion of convexity. The approach is based on the notion of pseudo-barycenter of an ordered n-tuple of points.
A "hidden" characterization of approximatively polyhedral convex sets in Banach spaces
Taras Banakh, Ivan Hetman (2012)
Studia Mathematica
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A closed convex subset C of a Banach space X is called approximatively polyhedral if for each ε > 0 there is a polyhedral (= intersection of finitely many closed half-spaces) convex set P ⊂ X at Hausdorff distance < ε from C. We characterize approximatively polyhedral convex sets in Banach spaces and apply the characterization to show that a connected component of the space of closed convex subsets of X endowed with the Hausdorff metric is separable if and only if contains a...