Functional means are a way of inducing a mean Mf from a differentiable function f.
If f(x) = x2, Mf(x, y) = (x + y)/2 is the arithmetic mean.
If f(x) = 1/x, Mf(x, y) = √(xy) is the geometric mean.
Seems like this should be useful for something.
Related post: Means and inequalities