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Journal of Convex Analysis 14 (2007), No. 2, 345--351
Copyright Heldermann Verlag 2007

Centrally Symmetric Convex Sets

Vladimir G. Boltyanski
CIMAT, A.P. 402, 36000 Guanajuato, Gto., Mexico

J. Jerónimo Castro
CIMAT, A.P. 402, 36000 Guanajuato, Gto., Mexico

There are some conditions under which a compact, convex set is centrally symmetric. The conditions were established by W. Blaschke and G. Hessenberg [Jahresberichte Deutsch. Math. Vereinigung 26 (1917) 215--220], G. D. Chakerian and M. S. Klamkin [Amer. Math. Monthly 111 (2004) 903--905], and L. Montejano [Bol. Soc. Mat. Mex. 38 (1993) 1--7]. In this article we give some new conditions.

Keywords: Convex set, symmetry, sections and projections of sets.

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