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Jul 8, 2016 at 13:05 comment added Suvrit ++ Another beautiful inequality proof by Fedor!
Jul 8, 2016 at 6:51 comment added Fedor Petrov Karamata's inequality (for any convex functions $\varphi$) is known to be a criterion of majorization. Just apply it to the convex functions $\max(x-T,0)$ with all $T$. I think, it must be written explicitly in standard references like Marshall-Olkin. en.m.wikipedia.org/wiki/Karamata%27s_inequality
Jul 8, 2016 at 2:19 comment added Igor Pak I am slightly confused by the "array $(h)$ majorates array $(q)$" implication. Is it standard that if the inequality holds for all $\varphi$, then there is an ordering?
Jul 7, 2016 at 23:49 vote accept Igor Pak
Jul 7, 2016 at 23:49 history edited Igor Pak CC BY-SA 3.0
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Jul 7, 2016 at 22:37 history edited Fedor Petrov CC BY-SA 3.0
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Jul 7, 2016 at 21:48 history edited Fedor Petrov CC BY-SA 3.0
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Jul 7, 2016 at 21:14 history edited Igor Pak CC BY-SA 3.0
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Jul 7, 2016 at 20:56 history answered Fedor Petrov CC BY-SA 3.0