Families of convex sets closed under intersections, homotheties and uniting increasing sequences of sets
Marek Lassak (1984)
Fundamenta Mathematicae
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Marek Lassak (1984)
Fundamenta Mathematicae
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Roversi, M.S.M., Chiacchio, A.O., Queiroz, M.L.B. (1996)
Portugaliae Mathematica
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Nachbin, Leopoldo (1993)
Portugaliae mathematica
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Postolică, Vasile (2004)
International Journal of Mathematics and Mathematical Sciences
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Ehrhard Behrends (2000)
Studia Mathematica
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The paper begins with a self-contained and short development of Bárány’s theorems of Carathéodory and Helly type in finite-dimensional spaces together with some new variants. In the second half the possible generalizations of these results to arbitrary Banach spaces are investigated. The Carathéodory-Bárány theorem has a counterpart in arbitrary dimensions under suitable uniform compactness or uniform boundedness conditions. The proper generalization of the Helly-Bárány theorem reads...
Zippin, M. (2000)
Serdica Mathematical Journal
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∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany). The space K[0, 1] of differences of convex functions on the closed interval [0, 1] is investigated as a dual Banach space. It is proved that a continuous function f on [0, 1] belongs to K[0, 1] ...
Berman, Abraham, Tarsy, Michael (1978)
International Journal of Mathematics and Mathematical Sciences
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Cel, Jaroslav (1999)
Beiträge zur Algebra und Geometrie
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Stanisław Kryński (1993)
Studia Mathematica
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Properties of metrically convex functions in normed spaces (of any dimension) are considered. The main result, Theorem 4.2, gives necessary and sufficient conditions for a function to be metrically convex, expressed in terms of the classical convexity theory.
A. L. Brown, H. L. Vasudeva
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The paper is concerned with the Fréchet differentiability and operator convexity of the operator functions on sets of self-adjoint operators on finite-dimensional inner product spaces which are associated with real-valued functions of one or two variables. In Part I it is shown that if a real-valued function is L times continuously differentiable then the associated operator functions are L times Fréchet differentiable with continuous Fréchet derivatives. It is shown that the operator...
Z. Kominek, M. Kuczma (1991)
Annales Polonici Mathematici
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