Hello,

I have this inequality I need to prove:

$\displaystyle

(1+\delta)(x-y)-(x^{1+\delta}-y^{1+\delta})+(x-y)^{1+\delta}\geq0$, where $\displaystyle 0\leq y < x \leq 1$ and $\displaystyle 0<\delta<1$.

I am not actually sure if it is correct, I just checked it numerically and was unable to find a counterexample.

Any ideas would be appreciated.