Geodesic
Moduli of local uniform rotundity for convex bodies in normed spaces
Canadian mathematical bulletin, Tome 68 (2025) no. 4, pp. 1251-1261

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DOI

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 $x\in \partial C$, that extend in a natural way the corresponding notions for the unit ball $B_X$, and we prove that they all coincide. This extends a known result of J. Daneš from 1976 concerning the particular case when $C=B_X$.
DOI : 10.4153/S0008439525000414
Mots-clés : Normed linear space, modulus of uniform rotundity, modulus of local uniform rotundity, convex body, point of local uniform rotundity 
Bernardi, Carlo Alberto De; Veselý, Libor. Moduli of local uniform rotundity for convex bodies in normed spaces. Canadian mathematical bulletin, Tome 68 (2025) no. 4, pp. 1251-1261. doi: 10.4153/S0008439525000414
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     title = {Moduli of local uniform rotundity for convex bodies in normed spaces},
     journal = {Canadian mathematical bulletin},
     pages = {1251--1261},
     year = {2025},
     volume = {68},
     number = {4},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439525000414/}
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