On solutions of Aczél's equation and some related equations (Q623417)

The authors consider the functional equation which is a generalization of the functional equation introduced by J. Aczél and so- called Gołąb-Schinzel functional equation. They present results on continuous on rays solutions of the equation \[ f[x+M(f(x))y] f(x) f(y) [f(x+M(f(x))y)- f(x) f(y)]= 0 \] and as a consequence get some results for Aczél and Gołąb-Schinzel functional equations. The methods of proofs are just standard methods for functional equations in several variables.