Sum form equations of multiplicative type
All solutions \(f\) are obtained of the sum form equation of multiplicative type \(f(pq) + f((1 - p)q) = f(q) \{m(p) + m(1 - p)\} + M(q) \{f(p) + f(1 - p)\}\), where \(p,q \in ]0,1[\) and \(m,M:\) \(]0,1[ \to \mathbb{R}\) are multiplicative functions. This type of functional equation is encountered in the characterization of measures of information.
sum form equation of multiplicative type
scientific article; zbMATH DE number 508715