Stolarsky's Inequality

If $0\leq g(x)\leq 1$ and $g$ is nonincreasing on the Interval [0,1], then for all possible values of $a$ and $b$,

$$\int_0^1 g(x^{1/(a+b)})\,dx\geq \int_0^1 g(x^{1/a})\,dx \int_0^1 g(x^{1/b})\,dx.$$