Difference between revisions of "Power Mean Inequality"
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=== The Mean === | === The Mean === | ||
| − | The power mean inequality is a generalized form of the multi-variable | + | The power mean inequality is a generalized form of the multi-variable [[Arithmetic Mean-Geometric Mean]] Inequality. |
The kth "Power Mean", with exponent k and a series (a_i) of positive real numbers is , | The kth "Power Mean", with exponent k and a series (a_i) of positive real numbers is , | ||
Revision as of 13:41, 11 July 2006
The Mean
The power mean inequality is a generalized form of the multi-variable Arithmetic Mean-Geometric Mean Inequality.
The kth "Power Mean", with exponent k and a series (a_i) of positive real numbers is ,
(The case k=0 is taken to be the geometic mean)
Inequality
If a < b, then M(a) ≤ M(b). Equality if and only if a1 = a2 = ... = an, following from 
proved with Jensen's inequality.
