On the level sum of two convex functions on Banach spaces.
Traoré, S., Volle, M. (1996)
Journal of Convex Analysis
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Displaying similar documents to “Recognizing the topology of the space of closed convex subsets of a Banach space”
On the level sum of two convex functions on Banach spaces.
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. ...
On nested sequences of convex sets in Banach spaces
Jesús M. F. Castillo, Manuel González, Pier Luigi Papini (2014)
Studia Mathematica
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We study different aspects of the representation of weak*-compact convex sets of the bidual X** of a separable Banach space X via a nested sequence of closed convex bounded sets of X.
Antiproximinal ѕets in Banach ѕpaces
S. Cobzaş (1999)
Acta Universitatis Carolinae. Mathematica et Physica
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On the p-drop theorem, 1 ≤ p ≤∞.
Abdelhakim Maaden (2002)
Extracta Mathematicae
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Relative Commutants in Compact Convex Sets and Banach Spaces.
Charles J.K. Batty (1979)
Mathematische Zeitschrift
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Convex-compact sets and Banach discs
I. Monterde, Vicente Montesinos (2009)
Czechoslovak Mathematical Journal
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Every relatively convex-compact convex subset of a locally convex space is contained in a Banach disc. Moreover, an upper bound for the class of sets which are contained in a Banach disc is presented. If the topological dual of a locally convex space is the -closure of the union of countably many -relatively countably compacts sets, then every weakly (relatively) convex-compact set is weakly (relatively) compact.
On Bárány's theorems of Carathéodory and Helly type
Ehrhard Behrends (2000)
Studia Mathematica
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The paper begins with a self-contained and short development of Bárány’s theorems of Carathéodory and Helly type in finite-dimensional spaces together with some new variants. In the second half the possible generalizations of these results to arbitrary Banach spaces are investigated. The Carathéodory-Bárány theorem has a counterpart in arbitrary dimensions under suitable uniform compactness or uniform boundedness conditions. The proper generalization of the Helly-Bárány theorem reads...
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...
Paraconvex functions and paraconvex sets
Huynh Van Ngai, Jean-Paul Penot (2008)
Studia Mathematica
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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....
Convex inequalities and the Hahn-Banach Theorem
Hoang Tu Y
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CONTENTSIntroduction............................................................................................................................................................................... 5§ 1. Finite systems of convex inequalities.......................................................................................................................... 6§ 2. Infinite systems of convex inequalities...........................................................................................................................