Geodesic
Local U-Convexity
Journal of convex analysis, Tome 18 (2011) no. 3, pp. 811-821

Voir la notice de l'article provenant de la source Heldermann Verlag

K.-S. Lau ["Best approximation by closed sets in Banach spaces", J. Approx. Theory 23 (1978) 29--36] considered the notion of "U-convex spaces" (originally called U-spaces) and showed that both uniform convexity and uniform smoothness imply U-convexity. Also U-convex spaces are uniformly non-square and hence super-reflexive. In this paper we introduce local U-convexity. It is shown that there are two possible localization of U-convexity. We derive our results quantitatively, that is, by the properties of modulus functions. Relationship to modulus of (local) uniform convexity is established and its consequences are discussed.
Classification : 46B20
Mots-clés : Locally uniformly convex, super-reflexive spaces, U-convexity 
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     author = {S. Dutta and B.-L. Lin},
     title = {Local {U-Convexity}},
     journal = {Journal of convex analysis},
     pages = {811--821},
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     volume = {18},
     number = {3},
     year = {2011},
     url = {http://geodesic.mathdoc.fr/item/JCA_2011_18_3_JCA_2011_18_3_a12/}
}
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S. Dutta; B.-L. Lin. Local U-Convexity. Journal of convex analysis, Tome 18 (2011) no. 3, pp. 811-821. http://geodesic.mathdoc.fr/item/JCA_2011_18_3_JCA_2011_18_3_a12/