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 Fr & eacute;chet differentiability of the metric projection operator onto closed balls centred at the origin in Hilbert spaces, which are given by Li in [Strict Fr & eacute;chet 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 Fr & eacute;chet differentiability of the metric projection operator onto closed balls with centre at arbitrarily given point in Hilbert spaces. Finally, we study the strict Fr & eacute;chet differentiability of the metric projection operator onto a second-order cone in Euclidean spaces.