Geodesic
Banach Spaces that are Uniformly Rotund in Weakly Compact Sets of Directions
Canadian journal of mathematics, Tome 29 (1977) no. 5, pp. 963-970

Voir la notice de l'article provenant de la source Cambridge University Press

In a Banach space, the directional modulus of rotundity, δ (ε, z), measures the minimum depth at which the midpoints of all chords of the unit ball which are parallel to z and of length at least ε are buried beneath the surface. A Banach space is uniformly rotund in every direction (URED) if δ (ε, z) is positive for every positive ε and every nonzero element z. This concept of directionalized uniform rotundity was introduced by Garkavi [6] to characterize those Banach spaces in which every bounded subset has at most one Čebyšev center. 
Smith, Mark A. Banach Spaces that are Uniformly Rotund in Weakly Compact Sets of Directions. Canadian journal of mathematics, Tome 29 (1977) no. 5, pp. 963-970. doi: 10.4153/CJM-1977-097-6
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