An inconsistency equation involving means
Tom 115 / 2009
Colloquium Mathematicum 115 (2009), 87-99
MSC: Primary 39B22; Secondary 26A24.
DOI: 10.4064/cm115-1-8
Streszczenie
We show that any quasi-arithmetic mean $A_{\varphi}$ and any non-quasi-arithmetic mean $M$ (reasonably regular) are inconsistent in the sense that the only solutions $f$ of both equations $$ f(M(x,y)) = A_{\varphi}(f(x), f(y)) $$ and $$ f(A_{\varphi}(x,y)) = M(f(x), f(y)) $$ are the constant ones.
