Geodesic
$\rho$-Continuity of a~metric projection onto convex closed sets
Matematičeskie zametki, Tome 23 (1978) no. 6, pp. 845-854.

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The linear normed spaces are characterized for which the metric projection onto every nonempty convex closed set is $\rho$-continuous. Some sufficient conditions are obtained for $H$-continuity of a metric projection. 
@article{MZM_1978_23_6_a6,
     author = {N. V. Nevesenko},
     title = {$\rho${-Continuity} of a~metric projection onto convex closed sets},
     journal = {Matemati\v{c}eskie zametki},
     pages = {845--854},
     publisher = {mathdoc},
     volume = {23},
     number = {6},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_6_a6/}
}
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N. V. Nevesenko. $\rho$-Continuity of a~metric projection onto convex closed sets. Matematičeskie zametki, Tome 23 (1978) no. 6, pp. 845-854. http://geodesic.mathdoc.fr/item/MZM_1978_23_6_a6/