Strict Fréchet differentiability of metric projection operators in Hilbert spaces

In this paper, we prove strict Frchet differentiability of the metric projection operator onto closed balls in Hilbert spaces and onto positive cones in Euclidean spaces.We find the exact expressions for Frchet derivatives.Since Frchet differentiability implies Gteaux directional differentiability, the results obtained in this paper strengthen some recent results obtained on the directional differentiability of the metric projection operator onto closed balls in Hilbert spaces and positive cones in Euclidean spaces and in l 2 , a Hilbert space.