Examples
- If we take to be the real line and, (or indeed any linear function, not equal to 0) then the f-mean corresponds to the arithmetic mean.
- If we take to be the set of positive real numbers and, then the f-mean corresponds to the geometric mean. According to the f-mean properties, the result does not depend on the base of the logarithm as long as it is positive and not 1.
- If we take to be the set of positive real numbers and, then the f-mean corresponds to the harmonic mean.
- If we take to be the set of positive real numbers and, then the f-mean corresponds to the power mean with exponent .
Read more about this topic: Quasi-arithmetic Mean
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