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In this paper, we prove strict Frechet differentiability of the metricprojection operator onto closed balls in Hilbert spaces, and we find exactexpressions for Frechet derivatives. Since Frechet differentiability impliesGateaux directional differentiability, the results obtained in this paperstrengthens the results in [8] and [10] about the directional differentiabilityof the metric projection operator onto closed balls in Hilbert spaces. We applythe Frechet differentiability of the metric projection onto closed balls inHilbert spaces to study the generalized differentiability of the metricprojection operator.

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