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Fundamentalnaya i Prikladnaya Matematika, 2012, Volume 17, Issue 4, Pages 3–12
(Mi fpm1418)
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This article is cited in 9 scientific papers (total in 9 papers)
Separation of convex sets by extreme hyperplanes
A. R. Alimov, V. Yu. Protasov M. V. Lomonosov Moscow State University
Abstract:
The problem of separation of convex sets by extreme hyperplanes (functionals) in normed linear spaces is examined. A concept of a bar (a closed set of a special form) is introduced; it is shown that a bar is characterized by the property that any point not lying in it can be separated from it by an extreme hyperplane. In two-dimensional spaces, in spaces with strictly convex dual, and in the space of continuous functions, any two bars are extremely separated. This property is shown to fail in the space of summable functions. A number of examples and generalizations are given.
Citation:
A. R. Alimov, V. Yu. Protasov, “Separation of convex sets by extreme hyperplanes”, Fundam. Prikl. Mat., 17:4 (2012), 3–12; J. Math. Sci., 191:5 (2013), 599–604
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Abstract page: | 763 | Full-text PDF : | 331 | References: | 67 | First page: | 2 |
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