Chisini mean

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In mathematics, a function f of n variables

x₁, ..., x_n

leads to a Chisini mean M if for every vector <x₁ ... x_n>, there exists a unique M such that

f(M,M, ..., M) = f(x₁,x₂, ..., x_n).

The arithmetic, harmonic, geometric, generalised, Heronian and quadratic means are all Chisini means, as are the weighted variants thereof.

[edit] Reference

They were introduced by Oscar Chisini, in the paper Chisini, O. "Sul concetto di media." Periodico di Matematiche 4, 106-116, 1929.