# zbMATH — the first resource for mathematics

Set-valued version of Sincov’s functional equation. (English) Zbl 1095.39021
Let $$X$$ be a nonempty set and let $$Y$$ be an Abelian semigroup. The functional equation $$F(x,y) + F(y,z)=F(x,z)$$, where $$F: X \times X \to 2^Y \backslash \{\emptyset\}$$ is an unknown set-valued mapping, is called the set-valued version of Sincov’s functional equation. The author shows that the set $$F(x,x)$$ does not depend on the choice of $$x$$ and investigates selections of the above functional equation.

##### MSC:
 39B52 Functional equations for functions with more general domains and/or ranges 39B82 Stability, separation, extension, and related topics for functional equations
Full Text: