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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
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