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On a functional equation of Alsina and García-Roig. (English) Zbl 0912.39010
The author determines, for every fixed \( p \in ]0,1[ \), the general solution \( f : I \to {\mathbb R} \) of the functional equation \[ f(px + (1-p)y) f((1-p)x + py) = f(x) f(y) \qquad (x,y \in I), \] supposing that \(f\) is different from zero on a set of positive Lebesgue measures. The main theorem (Theorem 2) provides a generalization of a result of W. Jarczyk and M. Sablik [Result. in Math. 26, No. 3-4, 324-335 (1994; Zbl 0829.39008)].

MSC:
39B22 Functional equations for real functions
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