-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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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.
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...
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 (1997)
Studia Mathematica
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The existence of a minimal element in every equivalence class of pairs of bounded closed convex sets in a reflexive locally convex topological vector space is proved. An example of a non-reflexive Banach space with an equivalence class containing no minimal element is presented.
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...
Pallaschke, Diethard, Urbański, Ryszard (1996)
Journal of Convex Analysis
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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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Siniša Vrećica (1981)
Publications de l'Institut Mathématique
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Josip E. Pečarić (1980)
Publications de l'Institut Mathématique
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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.
Zyskowski, Janusz (2015-11-13T12:11:38Z)
Acta Universitatis Lodziensis. Folia Mathematica
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Yannis Tsertos (2005)
Banach Center Publications
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Given a locally convex space (V,Γ), we find (all) the multiplications π on V (associative or not) such that the algebra A ≡ (V,π,Γ) becomes (i) A-convex, (ii) lm-convex.
Kurz, Sascha (2008)
Beiträge zur Algebra und Geometrie
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