Let C be a convex body (i.e., a proper closed convex subset with nonempty interior) in a normed space X. We consider four moduli of local uniform rotundity for C at a given point x ∂C, that extend in a natural way the corresponding notions for the unit ball BX , and we prove that they all coincide. This extends a known result of J. Daneš from 1976 concerning the particular case when C=BX.
Moduli of local uniform rotundity for convex bodies in normed spaces / C.A. De Bernardi, L. Veselý. - In: CANADIAN MATHEMATICAL BULLETIN. - ISSN 0008-4395. - 68:4(2025 Dec), pp. 1251-1261. [10.4153/s0008439525000414]
Moduli of local uniform rotundity for convex bodies in normed spaces
C.A. De Bernardi
Primo
;
2025
Abstract
Let C be a convex body (i.e., a proper closed convex subset with nonempty interior) in a normed space X. We consider four moduli of local uniform rotundity for C at a given point x ∂C, that extend in a natural way the corresponding notions for the unit ball BX , and we prove that they all coincide. This extends a known result of J. Daneš from 1976 concerning the particular case when C=BX.
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