Minkowski Inequality

Minkowski Inequality states:

Let $r>s$ be a nonzero real number, then for any positive numbers $a_{ij}$ , the following inequality holds:

$\left(\sum_{j=1}^{m}\left(\sum_{i=1}^{n}a_{ij}^r\right)^{s/r}\right)^{1/s}\geq \left(\sum_{i=1}^{n}\left(\sum_{j=1}^{m}a_{ij}^s\right)^{r/s}\right)^{1/r}$

Notice that if one of $r,s$ is zero, the inequality is equivalent to Holder's Inequality.

Problems

AIME 1991 Problem 15

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Minkowski Inequality

Problems