Some Results on the Strict Fréchet Differentiability of the Metric Projection Operator in Hilbert Spaces

In this paper, we first present a simpler proof of a result on the strict Fréchet differentiability of the metric projection operator onto closed balls centered at the origin in Hilbert spaces, which given by Li in \cite{Li24}. Then, based on this result, we prove the strict Fréchet differentiability of the metric projection operator onto closed balls with center at arbitrarily given point in Hilbert spaces. Finally, we study the strict Fréchet differentiability of the metric projection operator onto the second-order cones in Euclidean spaces.