Geodesic
On~the continuity of metric projection in Banach space
Sbornik. Mathematics, Tome 9 (1969) no. 2, pp. 171-182

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Two kinds of continuity and of metric projection are considered. For each type of continuity in the class of reflexive Banach spaces, necessary and sufficient conditions are given for the metric projection on each closed convex set to be continuous. In addition, some extensions of these results are given for nonreflexive spaces. Bibliography: 16 titles. 
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     author = {E. V. Oshman},
     title = {On~the continuity of metric projection in {Banach} space},
     journal = {Sbornik. Mathematics},
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     volume = {9},
     number = {2},
     year = {1969},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1969_9_2_a2/}
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E. V. Oshman. On~the continuity of metric projection in Banach space. Sbornik. Mathematics, Tome 9 (1969) no. 2, pp. 171-182. http://geodesic.mathdoc.fr/item/SM_1969_9_2_a2/