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 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.
De Bernardi, C. A., Veselý, L., Moduli of local uniform rotundity for convex bodies in normed spaces, <<CANADIAN MATHEMATICAL BULLETIN>>, 2025; (2025): N/A-N/A. [doi:10.4153/S0008439525000414] [https://hdl.handle.net/10807/313584]
Moduli of local uniform rotundity for convex bodies in normed spaces
De Bernardi, Carlo Alberto
;
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 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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
