So I need to proof the following inequality
If i start it by induction, I get to a point where I have to proove that
(with the first part)
And I have no idea where to go from here. Any suggestions?
Another possible approach, without induction :
Using the properties of the integral,
Summing these inequalities for gives
The right hand side can be rewritten as hence .
As , here is the first inequality : .
Using the same method, one can show the other one.