$f(t)={\displaystyle \prod_{j=1}^{d}(1+tb_{j})^{\alpha}}$ is my function.
Here, the statement says :
If $\alpha\leq\frac{1}{d}$, all $b_{j}>0$, and $t\in[0,1]$, then $f(t)={\displaystyle \prod_{j=1}^{d}(1+tb_{j})^{\alpha}}$ is concave.
I don't know how I can describe this. I know the definition of concavity which is here : https://en.wikipedia.org/wiki/Concave_function
My friend said it is all about 'sub-linearlity' I don't know what this is. Thanks in advance.
My guess : $(1+tb)^{\alpha}$ is concave when $\alpha<1$. Is this related to this problem?