Geodesic
Characterizations of Prox-Regular Sets in Uniformly Convex Banach Spaces
Journal of convex analysis, Tome 13 (2006) no. 3, pp. 525-559.

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

The aim of the paper is to extend to the setting of uniformly convex Banach spaces the results obtained for prox-regular sets in Hilbert spaces. Prox-regularity of a set C at a point x of C is a variational condition related to normal vectors and which is common to many types of sets. In the context of uniformly convex Banach spaces, the prox-regularity of a closed set C at x is shown to be still equivalent to the property of the distance function dC to be continuously differentiable outside of C on some neighbourhood of x. Additional characterizations are provided in terms of metric projection mapping. We also examine the global level of prox-regularity corresponding to the continuous differentiability of the distance function dC over an open tube of uniform thickness around the set C.
Classification : 49J52, 58C06, 58C20, 90C30
Mots-clés : Distance function, metric projection mapping, uniformly convex Banach space, variational analysis, proximal normal, prox-regular set 
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     title = {Characterizations of {Prox-Regular} {Sets} in {Uniformly} {Convex} {Banach} {Spaces}},
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     pages = {525--559},
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F. Bernard; L. Thibault; N. Zlateva. Characterizations of Prox-Regular Sets in Uniformly Convex Banach Spaces. Journal of convex analysis, Tome 13 (2006) no. 3, pp. 525-559. http://geodesic.mathdoc.fr/item/JCA_2006_13_3_JCA_2006_13_3_a4/