Assume $x \in \mathbb{R}$. In the wiki page, one property of strongly convex functions $f(x)$ is that it satisfies:
$f''(x)\geq m > 0~\forall x$ with with parameter $m > 0$.
Given $f(x) =e^x$, since $lim_{x\to -\infty} f''(x) = 0$ does this mean that exponential is not strongly convex?
From the Wikipedia page on Convex function:
The exponential function $f(x)=e^x$ is convex. It is also strictly convex, since $f''(x)=e^x>0$, but it is not strongly convex since the second derivative can be arbitrarily close to zero. More generally, the function $g(x)=e^{f(x)}$ is logarithmically convex if $f$ is a convex function. The term superconvex is sometimes used instead.
