Displaying similar documents to “Minimal pairs of bounded closed convex sets”

Minimal pairs of compact convex sets

Diethard Pallaschke, Ryszard Urbański (2004)

Banach Center Publications

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Pairs of compact convex sets naturally arise in quasidifferential calculus as sub- and superdifferentials of a quasidifferentiable function (see Dem86). Since the sub- and superdifferentials are not uniquely determined, minimal representations are of special importance. In this paper we give a survey on some recent results on minimal pairs of closed bounded convex sets in a topological vector space (see PALURB). Particular attention is paid to the problem of characterizing minimal representatives...

Minimal pairs of bounded closed convex sets as minimal representations of elements of the Minkowski-Rådström-Hörmander spaces

Jerzy Grzybowski, Diethard Pallaschke, Ryszard Urbański (2009)

Banach Center Publications

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The theory of minimal pairs of bounded closed convex sets was treated extensively in the book authored by D. Pallaschke and R. Urbański, Pairs of Compact Convex Sets, Fractional Arithmetic with Convex Sets. In the present paper we summarize the known results, generalize some of them and add new ones.

On reduced pairs of bounded closed convex sets.

Jerzy Grzybowski, Ryszard Urbanski (2003)

Revista Matemática Complutense

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In this paper certain criteria for reduced pairs of bounded closed convex set are presented. Some examples of reduced and not reduced pairs are enclosed.

On the reduction of pairs of bounded closed convex sets

J. Grzybowski, D. Pallaschke, R. Urbański (2008)

Studia Mathematica

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Let X be a Hausdorff topological vector space. For nonempty bounded closed convex sets A,B,C,D ⊂ X we denote by A ∔ B the closure of the algebraic sum A + B, and call the pairs (A,B) and (C,D) equivalent if A ∔ D = B ∔ C. We prove two main theorems on reduction of equivalent pairs. The first theorem implies that, in a finite-dimensional space, a pair of nonempty compact convex sets with a piecewise smooth boundary and parallel tangent spaces at some boundary points is not minimal. The...

Pairs of sets with convex union.

Ryszard Urbanski (1997)

Collectanea Mathematica

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In this paper the notion of convex pairs of convex bounded subsets of a Hausdorff topological vector space is introduced. Criteria of convexity pair are proved.

Minimality in asymmetry classes

Michał Wiernowolski (1997)

Studia Mathematica

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We examine minimality in asymmetry classes of convex compact sets with respect to inclusion. We prove that each class has a minimal element. Moreover, we show there is a connection between asymmetry classes and the Rådström-Hörmander lattice. This is used to present an alternative solution to the problem of minimality posed by G. Ewald and G. C. Shephard in [4].