Christensen measurable solutions of some functional equation
Given a separable \(F\)-space \(X\) over the field \(K\) of reals or complex numbers, the author finds the solutions of the functional equation \[ f(x + M(f(x))y) = f(x) f(y) \] in the class of functions \(M: K \to K\) and Christensen measurable function \(f: X \to K\). This equation generalizes the classical Cauchy's equation for the exponential function (\(M \equiv 1) \) and the Goląb-Schinzel equation (\(M=j_K\)).
scientific article; zbMATH DE number 5666159
scientific article