Properties of typical bounded closed convex sets in Hilbert space.

de Blasi, F.S.; Zhivkov, N.V.

Displaying similar documents to “Properties of typical bounded closed convex sets in Hilbert space.”

On Typical Compact Convex Sets in Hilbert Spaces

De Blasi, F. (1997)

Serdica Mathematical Journal

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Let E be an infinite dimensional separable space and for e ∈ E and X a nonempty compact convex subset of E, let qX(e) be the metric antiprojection of e on X. Let n ≥ 2 be an arbitrary integer. It is shown that for a typical (in the sence of the Baire category) compact convex set X ⊂ E the metric antiprojection qX(e) has cardinality at least n for every e in a dense subset of E.

Ambiguous loci of the farthest distance mapping from compact convex sets

F. De Blasi, J. Myjak (1995)

Studia Mathematica

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Let be a strictly convex separable Banach space of dimension at least 2. Let K() be the space of all nonempty compact convex subsets of endowed with the Hausdorff distance. Denote by $K^{0}$ the set of all X ∈ K() such that the farthest distance mapping $a \mapsto M_{X} (a)$ is multivalued on a dense subset of . It is proved that $K^{0}$ is a residual dense subset of K().

Generic well-posedness in some classes of optimization problems

Julian Petrov Revalski (1987)

Acta Universitatis Carolinae. Mathematica et Physica

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Best proximity pairs theorems for continuous set-valued maps.

Amini-Harandi, A., Farajzadeh, A.P., O&#039;Regan, D., Agarwal, R.P. (2008)

Fixed Point Theory and Applications [electronic only]

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The Demyanov metric and some other metrics in the family of convex sets

Tadeusz Rzeżuchowski (2012)

Open Mathematics

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We describe some known metrics in the family of convex sets which are stronger than the Hausdorff metric and propose a new one. These stronger metrics preserve in some sense the facial structure of convex sets under small changes of sets.

Generic well-posedness in minimization problems.

Ioffe, A., Lucchetti, R.E. (2005)

Abstract and Applied Analysis

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On convex metric spaces V

R. Duda (1970)

Fundamenta Mathematicae

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Boundaries of convex sets.

M. Valdivia (1993)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

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On almost coincidence points in generalized convex spaces.

Mitrović, Zoran D. (2006)

Fixed Point Theory and Applications [electronic only]

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Some geometric properties of typical compact convex sets in Hilbert spaces

F. de Blasi (1999)

Studia Mathematica

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An investigation is carried out of the compact convex sets X in an infinite-dimensional separable Hilbert space , for which the metric antiprojection $q_{X} (e)$ from e to X has fixed cardinality n+1 ( $n \subseteq ℕ$ arbitrary) for every e in a dense subset of . A similar study is performed in the case of the metric projection $p_{X} (e)$ from e to X where X is a compact subset of .