Let $g : \mathbb{N} \to [0, \infty)$ be an D4686: Unsigned real sequence.
The strict asymptotic upper bound growth class with respect to $g$ is the D11: Set \begin{equation} \left\{ f : \mathbb{N} \to \mathbb{R} \mid \forall \, \varepsilon > 0 : \exists \, n_0 \in \mathbb{N} : \forall \, n \geq n_0 : |f(n)| \leq \varepsilon g(n) \right\} \end{equation}