## 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

Zbl 0829.39008