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 centred at the origin in Hilbert spaces, which are given by Li in [Strict Fréchet differentiability of the metric projection operator in Hilbert spaces; 2024. Available from: https://arxiv.org/abs/2312.14362]. Then, based on this result, we prove the strict Fréchet differentiability of the metric projection operator onto closed balls with centre at arbitrarily given point in Hilbert spaces. Finally, we study the strict Fréchet differentiability of the metric projection operator onto a second-order cone in Euclidean spaces.