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Hyers-Ulam stability of additive set-valued functional equations. (English) Zbl 1220.39030
The authors prove the Hyers-Ulam stability of the additive set-valued functional equations $$f(\alpha x+\beta y)=rf(x)+sf(y)$$ and $$f(x+y+z)=2f\left(\frac{x+y}{2}\right)+f(z)$$, where $$\alpha >0$$, $$\beta >0$$, $$r,s \in \mathbb{R}$$ with $$\alpha+\beta=r+s\neq 1$$. See also T. Cardinali, K. Nikodem and F. Papalini [Ann. Pol. Math. 58, No. 2, 185–192 (1993; Zbl 0786.26016)].

##### MSC:
 39B82 Stability, separation, extension, and related topics for functional equations 39B72 Systems of functional equations and inequalities
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##### References:
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