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Hyers-Ulam stability of a generalized additive set-valued functional equation. (English) Zbl 1282.39030
Summary: We define a generalized additive set-valued functional equation, which is related to the following generalized additive functional equation: \[ f(x_1+\dots+x_l)=(l-1)f\left(\frac{x_1 + \dots+x_{l-1}}{l-1}\right)+f(x_l) \] for a fixed integer \(l\) with \(l > 1\), and prove the Hyers-Ulam stability of the generalized additive set-valued functional equation.

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B55 Orthogonal additivity and other conditional functional equations
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