Geodesic
Sharp estimates for the moduli of continuity of metric projections onto weakly convex sets
Izvestiya. Mathematics , Tome 79 (2015) no. 4, pp. 668-697

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We study the dependence of metric projections on the following three parameters: the point projected, the set to which we are projecting, and the norm (generally speaking, non-symmetric) that determines the metric. We obtain sharp estimates for the moduli of continuity of metric projections onto convex and weakly convex sets in Banach spaces. We also estimate these moduli in terms of the moduli of convexity and smoothness of the space (or the quasi-ball).
Keywords: metric projection, weakly convex sets. 
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     author = {G. E. Ivanov},
     title = {Sharp estimates for the moduli of continuity of metric projections onto weakly convex sets},
     journal = {Izvestiya. Mathematics },
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     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2015_79_4_a1/}
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G. E. Ivanov. Sharp estimates for the moduli of continuity of metric projections onto weakly convex sets. Izvestiya. Mathematics , Tome 79 (2015) no. 4, pp. 668-697. http://geodesic.mathdoc.fr/item/IM2_2015_79_4_a1/