An inconsistency equation involving means
Volume 115 / 2009
Colloquium Mathematicum 115 (2009), 87-99
MSC: Primary 39B22; Secondary 26A24.
DOI: 10.4064/cm115-1-8
Abstract
We show that any quasi-arithmetic mean 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.
