Geodesic
An inconsistency equation involving means
Roman Ger1 ; Tomasz Kochanek1
1 Institute of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland
Colloquium Mathematicum, Tome 115 (2009) no. 1, pp. 87-99.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm115-1-8
Keywords: quasi arithmetic mean varphi non quasi arithmetic mean reasonably regular inconsistent sense only solutions equations y varphi varphi constant

Roman Ger 1 ; Tomasz Kochanek 1

1 Institute of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland 
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Roman Ger; Tomasz Kochanek. An inconsistency equation involving means. Colloquium Mathematicum, Tome 115 (2009) no. 1, pp. 87-99. doi : 10.4064/cm115-1-8. http://geodesic.mathdoc.fr/articles/10.4064/cm115-1-8/

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