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.
Keywords:
quasi arithmetic mean varphi non quasi arithmetic mean reasonably regular inconsistent sense only solutions equations y varphi varphi constant
Affiliations des auteurs :
Roman Ger
1
;
Tomasz Kochanek
1
1
Institute of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland
@article{10_4064_cm115_1_8,
author = {Roman Ger and Tomasz Kochanek},
title = {An inconsistency equation involving means},
journal = {Colloquium Mathematicum},
pages = {87--99},
year = {2009},
volume = {115},
number = {1},
doi = {10.4064/cm115-1-8},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm115-1-8/}
}
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AU - Tomasz Kochanek
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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
