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 September 10th, 2013, 05:55 AM #1 Newbie   Joined: May 2012 Posts: 8 Thanks: 0 A convex function question Hello! I was wondering whether there is a useful property that can be said about a general convex function $f$ 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, $x>1,y > 1, z > 1$and we have that $x \leq y \cdot z$. ($x$ and $z$ can be integers if that's more helpful, but I doubt it.) Now, for a general convex function $f$, we have that $f(x) \leq f(y \cdot z)$. My question is, is there a property that says $f(x) \leq f(y) \cdot f(z)$? (Note that "$\cdot$" is simply multiplication.) I could not find a counterexample for this, but I could easily find counterexamples to show that $f(x) > y \cdot f(z)$. Thanks for your help!
 September 10th, 2013, 06:31 AM #2 Newbie   Joined: May 2012 Posts: 8 Thanks: 0 Re: A convex function question I can never seem to find how to edit the post, so $x \geq 1$, $z \geq 1$, but $y > 1$.

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