On a functional equation of Alsina and García-Roig. (English) Zbl 0912.39010

Lajkó, Károly

Publ. Math. Debr. 52, No. 3-4, 507-515 (1998).

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)].

Reviewer: Zoltán Boros (Debrecen)

MSC:

39B22

Functional equations for real functions

Keywords:

functional equation; general solution; \(k\)-additive symmetric functions

Citations:

Zbl 0829.39008