Complementaries of Greek means with respect to Gini means.

*(English)*Zbl 1157.26324Summary: A mean $P$ is called invariant with respect to a pair of means $(M,N)$ if it is a solution of the generalized Gaussâ€™ functional equation

$$f\left(M\right(a,b),N(a,b\left)\right)=f(a,b),\phantom{\rule{1.em}{0ex}}a,b>0\xb7$$

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:

26E60 | Means |