  In this paper, we prove strict Frechet differentiability of the metric
projection operator onto closed balls in Hilbert spaces, and we find exact
expressions for Frechet derivatives. Since Frechet differentiability implies
Gateaux directional differentiability, the results obtained in this paper
strengthens the results in [8] and [10] about the directional differentiability
of the metric projection operator onto closed balls in Hilbert spaces. We apply
the Frechet differentiability of the metric projection onto closed balls in
Hilbert spaces to study the generalized differentiability of the metric
projection operator.
