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September 10th, 2013, 05:55 AM   #1
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A convex function question

Hello!

I was wondering whether there is a useful property that can be said about a general convex function given some relations. I've already tried to search engine about properties of functions in general, but I didn't come across anything that would answer my question.

Okay, so what we know is this. We have three positive real numbers, and we have that . ( and can be integers if that's more helpful, but I doubt it.) Now, for a general convex function , we have that . My question is, is there a property that says ? (Note that "" is simply multiplication.) I could not find a counterexample for this, but I could easily find counterexamples to show that .

Thanks for your help!
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September 10th, 2013, 06:31 AM   #2
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Re: A convex function question

I can never seem to find how to edit the post, so
, ,
but
.
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