Systems of generalized translation equations on a restricted domain (Q1888655)

Motivated by some functional models arising in the psychophysical theory the author considers the system of functional equations \[ F(x+t, y) = G( F(x,y), t) \quad\text{ and } \quad F(x, y+s) = H(F(x,y), s), \] where \(F\) is a continuous real valued function defined on a connected open subset of the plane which is strictly monotonic in one of its variables and \(F,G\) are real valued functions. It is proved that the solutions \(F\) can be represented in the form \( F(x,y) = f(ax+by) \), with a strictly monotonic function \(f\) of a single variable and real numbers \(a,b\). The techniques used for proving this representation theorem have their own interest.