An inconsistency equation involving means
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 and are the constant ones.
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 and are the constant ones.
We prove: If then The constant is the best possible.