I have the following condition of the function $f : \mathbb R \to \mathbb R$: $$\exists\, h:\mathbb R_+ \to \mathbb R_+ \text{ bijective s.t., } \forall s>0, \frac{\partial^2}{\partial^2 s}\left(\left.\frac{\partial^k}{\partial^kt} f\left(h(s)t\right)\right\rvert_{t = -1}\right) >0,\; \forall k \in \{0,\dotsc,n\}.$$

What does it mean for the function $f$?