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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.

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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