-minimal pairs of compact convex sets.
Pallaschke, D., Urbańska, W., Urbański, R. (1997)
Journal of Convex Analysis
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Pallaschke, D., Urbańska, W., Urbański, R. (1997)
Journal of Convex Analysis
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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.
J. Grzybowski, R. Urbański (2003)
Studia Mathematica
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Let [A,B] be the family of pairs of compact convex sets equivalent to (A,B). We prove that the cardinality of the set of minimal pairs in [A,B] that are not translates of one another is either 1 or greater than ℵ₀.
S. Owa, L. Liu, Wancang Ma (1989)
Matematički Vesnik
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Rade Živaljević (1979)
Publications de l'Institut Mathématique
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Josip E. Pečarić (1980)
Publications de l'Institut Mathématique
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Siniša Vrećica (1981)
Publications de l'Institut Mathématique
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Pallaschke, Diethard, Urbański, Ryszard (1997)
Journal of Convex Analysis
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Zyskowski, Janusz (2015-11-13T12:11:38Z)
Acta Universitatis Lodziensis. Folia Mathematica
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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...
H. R. Abdel-Gawad, D. K. Thomas (1991)
Publications de l'Institut Mathématique
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Kurz, Sascha (2008)
Beiträge zur Algebra und Geometrie
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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.
Moussafir, J.-O. (2000)
Zapiski Nauchnykh Seminarov POMI
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