Sequential derivatives and their application to a Sûto equation (Q5945046)

The author solves the functional equation \[ \varphi(x+y) ={f(x) g(y)+ h(x)\ell(y) \over m(x)+n(y)}, \] where the real valued, continuous functions \(\varphi,f,g, \dots,n\) are all unknown and defined over an arbitrary rectangle in \(\mathbb{R}^2\). For the proof differentiation techniques are used. The author states that this paper is closely related to his paper in [Aequations Math. 57, No. 2-3, 254-277 (1999; Zbl 0934.39009)].