Inequality to prove involving convex notions

Hi everyone,

Here's an exercice I have trouble with.

Let and define

I have to show that, assuming .

I have already tried a looooot of things. I think I'm suppose to use some convex inequalities : my first thought was to take the log of , but it didn't seem to end very well for me.

I've also tried to use other known inequalities, such as . But I don't think it works.

So know, it's been almost an hour I'm on it, and I would like to have a small hint : I do not want the whole answer but just a tips which can make me progress.

Thank you for your always-so-good answers,

Hugo.

Re: Inequality to prove involving convex notions

We have to show that for , we have . Take the -th power, and use .