Power Mean Inequality
The Mean
The Power Mean Inequality is a generalized form of the multi-variable Arithmetic Mean-Geometric Mean Inequality.
For a real number k and positive real numbers , the kth power mean of the
is
when and is given by the geometric mean of the
when
.
Inequality
If then
and equality holds if and only if
.
The Power Mean Inequality follows from the fact that together with Jensen's Inequality.