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JOURNALS // Izvestiya of Saratov University. Mathematics. Mechanics. Informatics // Archive

Izv. Saratov Univ. Math. Mech. Inform., 2014 Volume 14, Issue 4(2), Pages 489–497 (Mi isu540)

This article is cited in 16 papers

Mathematics

Convexity of Bounded Chebyshev Sets in Finite-dimensional Asymmetrically Normed Spaces

A. R. Alimov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, 1, Main Building, Leninskiye Gory, GSP-1, Moscow, 119991, Russia

Abstract: The well-known Tsar'kov's characterisation of finite-dimensional Banach spaces in which every bounded Chebyshev set (bounded $P$-acyclic set) is convex is extended to the asymmetrical setting.

Key words: bounded Chebyshev set, convexity, asymmetric norm.

UDC: 517.982.256

DOI: 10.18500/1816-9791-2014-14-4-489-497



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