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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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