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Complementaries of Greek means with respect to Gini means. (English) Zbl 1157.26324
Summary: A mean \(P\) is called invariant with respect to a pair of means \((M,N)\) if it is a solution of the generalized Gauss’ functional equation
\[ f(M(a,b),N(a,b))= f(a,b), \quad a,b>0. \]
Equivalently \(N\) is called complementary of \(M\) with respect to \(P\). Determining the complementary of a mean with respect to another mean gives the possibility of definition of a double sequence with known limit. We study the complementary of Greek means with respect to weighted Gini means in the family of Greek means.

26E60 Means