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.
| Original language | English |
|---|---|
| Pages (from-to) | N/A-N/A |
| Journal | Canadian Mathematical Bulletin |
| Issue number | 2025 |
| DOIs | |
| Publication status | Published - 2025 |
All Science Journal Classification (ASJC) codes
- General Mathematics
Keywords
- convex body
- modulus of local uniform rotundity
- modulus of uniform rotundity
- normed linear space
- point of local uniform rotundity
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