Strict Frechet and generalized differentiability of the metric projection operator onto balls in Hilbert spaces

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.