An inconsistency equation involving means

• Autorzy: Roman Ger , Tomasz Kochanek
• Języki publikacji: EN

Abstrakty

EN

We show that any quasi-arithmetic mean $A_{φ}$ and any non-quasi-arithmetic mean M (reasonably regular) are inconsistent in the sense that the only solutions f of both equations
$f(M(x,y)) = A_{φ}(f(x),f(y))$
and
$f(A_{φ}(x,y)) = M(f(x),f(y))$
are the constant ones.

Kategorie tematyczne

• 26A24: Differentiation (functions of one variable): general theory, generalized derivatives, mean-value theorems
• 39B22: Equations for real functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2009
• Tom: 115
• Numer: 1
• Strony: 87-99

Daty

wydano

2009

Twórcy

autor

Roman Ger

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

autor

Tomasz Kochanek

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

Identyfikatory

DOI

10.4064/cm115-1-8