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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.

##### MSC:
 2.6e+61 Means
##### Keywords:
Greek means; complementary means; Gini means