Sum form equations of multiplicative type. (English) Zbl 0823.39005
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.
Reviewer: P.N.Rathie (Brasilia)
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