Chisini mean

In mathematics, a function f of n variables x1, ..., xn leads to a Chisini mean M if, for every vector ⟨x1, ..., xn⟩, there exists a unique M such that[1]

f(M,M, ..., M) = f(x1,x2, ..., xn).

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

While Oscar Chisini was arguably the first to deal with "substitution means" in some depth in 1929,[1] the idea of defining a mean as above is quite old, appearing (for example) in early works of Augustus De Morgan.[2][original research?]

  1. ^ a b Cite error: The named reference graziani was invoked but never defined (see the help page).
  2. ^ De Morgan, Augustus. "Mean" in Penny Cyclopaedia (1839).