# Minkowski inequality

In the Wikipedia proof of the Minkowski inequality (http://en.wikipedia.org/wiki/Minkowski_inequality), the following inequality is used:
|f+g|p ≤ 2p-1(|f|p+|g|p).
I was just wondering if this inequality has a name or if this is too "first principles" to warrant a name.

Thanks!

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If I read the article correctly it's just using convexity. –  Michael Hoffman Nov 2 '09 at 7:53
Thanks Michael, I was under the impression that this was generally true! –  mornington Nov 2 '09 at 8:10
It is generally true. It is the composition of the triangle inequality |f+g| </= |f|+|g| composed with the power mean inequality (a+b)/2 </= ((a^p+b^p)/2)^(1/p) for a=|f| and b=|g| which is a consequence of convexity. –  Philipp Lampe Nov 2 '09 at 8:19
Thanks Philipp! –  mornington Nov 2 '09 at 8:29