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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),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.

MSC:
26E60Means