Power Mean Inequality
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.
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