Geodesic
Directional moduli of rotundity and smoothness
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 1, pp. 39-51.

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We study various notions of directional moduli of rotundity and when such moduli of rotundity of power type imply the underlying space is superreflexive. Duality with directional moduli of smoothness and some applications are also discussed.
Classification : 46B03, 46B20
Keywords: uniform rotundity; uniform smoothness; moduli of power type; superreflexive 
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Bartlett, Michael O.; Giles, John R.; Vanderwerff, Jon D. Directional moduli of rotundity and smoothness. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 1, pp. 39-51. http://geodesic.mathdoc.fr/item/CMUC_1999__40_1_a3/