Sequential derivatives and their application to a Sûto equation

Summary.

The functional equation¶$\varphi (x+ y) =\frac{f(x) g(y) + h(x) l(y)}{m(x) + n (y)}$,¶where the real valued, continuous functions $\varphi,f,g,\ldots,n$ are all unknown, is solved in an arbitrary rectangle in ${\Bbb R}^2$. The proof is based on differentiation. To do this without differentiability assumptions we have to use a concept of derivative, more flexible than the classical one.