Asymptotic equivalence-like relation

Question

Let $f, g: \mathbb R\to (0,\infty)$ such that $\cfrac{f(x)}{g(x)}$ is bounded both from below and above for all $x\in\mathbb R$.

Is there any name for this relation? (Like if $\cfrac{f(x)}{g(x)}$ would converge to 1 as $x\to\infty$, one would say that they are asymptotically equivalent.)

Answer 1

You are probably looking for the big-theta notation $$\forall x_0,\ f(x)=\Theta(g(x))\ x\to x_0$$ matches exactly with your definition