An inconsistency equation involving means

Roman Ger, and Tomasz Kochanek. "An inconsistency equation involving means." Colloquium Mathematicae 115.1 (2009): 87-99. <http://eudml.org/doc/283809>.

@article{RomanGer2009,
abstract = {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.},
author = {Roman Ger, Tomasz Kochanek},
journal = {Colloquium Mathematicae},
keywords = {generalized Jensen functional equation; quasi-arithmetic mean; logarithmic mean; bisymmetry equation},
language = {eng},
number = {1},
pages = {87-99},
title = {An inconsistency equation involving means},
url = {http://eudml.org/doc/283809},
volume = {115},
year = {2009},
}

TY - JOUR
AU - Roman Ger
AU - Tomasz Kochanek
TI - An inconsistency equation involving means
JO - Colloquium Mathematicae
PY - 2009
VL - 115
IS - 1
SP - 87
EP - 99
AB - 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.
LA - eng
KW - generalized Jensen functional equation; quasi-arithmetic mean; logarithmic mean; bisymmetry equation
UR - http://eudml.org/doc/283809
ER -