0
$\begingroup$

Question: Show that $(\frac{1}{n} \sum_{i=1}^n |x_i|^p)^{1/p} \ge \frac{1}{n} \sum_{i=1}^n |x_i|$ in which $p>1$, $x_i \in \mathbb{R}$, $i=1,2,\dots,n$

Could you give me some hint to solve this problem. I see that it like the Minkovski's inequality but it not true. Thank all!

$\endgroup$
1
  • $\begingroup$ Google Power Means Inequality... $\endgroup$
    – Macavity
    Jul 10, 2019 at 13:00

1 Answer 1

0
$\begingroup$

It can be easily showed by Weighted Power Mean. $\;$ You can see Weighted Power Mean by here on page $2$ https://artofproblemsolving.com/articles/files/MildorfInequalities.pdf

$\endgroup$

Not the answer you're looking for? Browse other questions tagged .