Data di Pubblicazione:
2024
Citazione:
Moduli of uniform convexity for convex sets / C.A. De Bernardi, L. Vesely. - In: ARCHIV DER MATHEMATIK. - ISSN 0003-889X. - (2024), pp. 1-10. [Epub ahead of print] [10.1007/s00013-024-02031-8]
Abstract:
Let C be a proper, closed subset with nonempty interior in a
normed space X. We define four variants of modulus of convexity for C
and prove that they all coincide. This result, which is classical and wellknown
for C = B_X (the unit ball of X), requires a less easy proof than
the particular case of B_X. We also show that if the modulus of convexity
of C is not identically null, then C is bounded. This extends a result by
M.V. Balashov and D. Repovs.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Normed linear space; Convex body; Uniformly convex set; Modulus of convexity;
Elenco autori:
C.A. De Bernardi, L. Vesely
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