Special cases of the functional equation\[h_{1}\left(\frac{x}{c\left(y\right)}\right)\frac{1}{c\left(y\right)}f_{Y}\left(y\right)=h_{2}\left(\frac{y}{d\left(x\right)}\right)\frac{1}{d\left(x\right)}f_{X}\left(x\right)\]are investigated for almost all$\left(x,y\right)\in\r^{2}_{+}$,for the given functions$c$, $d$and the unknown functions$h_{1}$, $h_{2}$,$f_{X}$ and $f_{Y}$.
@article{36,
title = {Functional equations stemming from probability theory},
journal = {Tatra Mountains Mathematical Publications},
volume = {43},
year = {2009},
doi = {10.2478/tatra.v44i0.36},
language = {EN},
url = {http://dml.mathdoc.fr/item/36}
}
Lajkó, Károly; Mészáros, Fruzsina. Functional equations stemming from probability theory. Tatra Mountains Mathematical Publications, Tome 43 (2009) . doi : 10.2478/tatra.v44i0.36. http://gdmltest.u-ga.fr/item/36/