Difference between revisions of "Power Mean Inequality"
Line 16: | Line 16: | ||
[[Category:Number theory]] | [[Category:Number theory]] | ||
[[Category:Theorems]] | [[Category:Theorems]] | ||
− |
Revision as of 08:31, 15 October 2007
The Power Mean Inequality is a generalized form of the multi-variable Arithmetic Mean-Geometric Mean Inequality.
Inequality
For a real number and positive real numbers
, the
th power mean of the
is
when
and is given by the geometric mean of the
when
.
For any finite set of positive reals, , we have that
implies
and equality holds if and only if
.
The Power Mean Inequality follows from the fact that together with Jensen's Inequality.
This article is a stub. Help us out by expanding it.