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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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References:
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