Sublinearity and concavity of a function

Question

Problem

A function $f$ is said to be sublinear in $n$ when $$\lim_{n\rightarrow \infty} \frac{f(n)}{c^n} =0\ (c > 0)$$ Some classical examples of sublinar function include $f(n)=\sqrt{n}$ and $f(n)=\log n$. Since these functions happen to be concave function in $n$. I am wondering whether there is relationship between the sublinearity and concavity of a function

Answer 1

No, take $f(n) = \sqrt{n}+\sin(n)$ as an example.