“…It is known (see, e.g., [22,Theorem 4.8 (8)]) that if 4ϕ 0 r < 1 and d(x, K) < r then the metric projection π K (x) = {y ∈ K : |y − x| = d(x, K)} is a singleton, which is Lipschitz with respect to x, and Lip(π K ) = 1 1−4ϕ0r . Moreover, if the diameter of K, diam K, is such that r = 2n n + 1 (ϕ 0 · diam K) 2 < 1 , then the metric projection π K from the convex hull of K, co K into K is a Lipschitz singlevalued map, with Lip(π K ) = 1/(1 − r) (see [18,Proposition 3.1] and [22,Theorem 4.8 (8)]). Actually in this case K is a retract of co K, with a special Lipschitz retraction, namely the metric projection (see also [24]).…”