ON THE INVARIANCE EQUATION FOR MEANS OF GENERALIZED POWER GROWTH

We generalize the result of (Witkowski, 2014) which binds orders of homogeneous, symmetric means M,N,K: , N , K : R-+(2) -> R + of power growth that satisfy the invariance equation K ( M ( x , y ) , N ( x , y )) =K(x,y) K ( x , y ) to the broader class of means. Moreover, we define the lower- and the upper-order which gives us insight into the order of the solution of this equation in the case when means do not belong to this class.