Displaying similar documents to “On the reduction of pairs of bounded closed convex sets”

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.

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.