Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Suppose we have functions $g\colon [0,1]\mapsto \mathbb{R}$, which is concave, vanishes at the origin and fullfills condition $$g(xy)/xy\leq g(x)/x+g(y)/y$$ for any $x,y\in[0,1]$ and $f\colon (0,\infty)\mapsto [0,1]$ which is convex and decreasing. Define function $h\colon [0,\infty)\mapsto \mathbb{R}$ as $$h(x):=g(f(x))/f(x).$$ Can it not be concave?

share|improve this question
@FF: Dear FF, please read the FAQ. I think this question is not suitable for MO, you might want to try posting it a math.stackexchange.com –  Chandrasekhar Apr 15 '13 at 10:00
add comment

Know someone who can answer? Share a link to this question via email, Google+, Twitter, or Facebook.

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.