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Stability of some set-valued functional equations. (English) Zbl 1236.39034
The authors consider the stability of some set-valued functional equations. Namely, they deal with mappings \(F\) defined on a cone and with closed and bounded subsets of a real vector space as values. It is proved that if \(F\) satisfies one of the inclusions: \[ F(x)+F(y)\subseteq 2F\left(\frac{x+y}{2}\right); \] \[ F(x+y)+F(x-y)\subseteq 2F(x)+2F(y); \] \[ F(2x+y)+F(2x-y)\subseteq 2F(x+y)+2F(x-y)+12F(x); \] \[ F(2x+y)+F(2x-y)+6F(y)\subseteq 4F(x+y)+4F(x-y)+24F(x), \] then it admits a unique additive, quadratic, cubic and quartic selection, respectively.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
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