Definition:Hölder Mean

Definition
Let $x_1, x_2, \ldots, x_n \in \R_{\ge 0}$ be positive real numbers.

Let $p$ be an extended real number.

The Hölder mean with exponent $p$ of $x_1, x_2, \ldots, x_n$ is denoted $\map {M_p} {x_1, x_2, \ldots, x_n}$.

Also see

 * Inequality of Hölder Means


 * Definition:Arithmetic Mean
 * Definition:Geometric Mean
 * Definition:Harmonic Mean


 * $p$-Norm