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On the generalized stability of d’Alembert functional equation. (English) Zbl 1296.39025
Summary: We study the super stability problem for the functional equation: $\sum_{\psi \in K_{n-1}} f (\psi (x_1,\dots, x_n)) = 2^{n-1} \prod_{i=1}^n f (x_i)$ on an abelian group and the unknown function $$f$$ is (complex or semi simple) Banach algebra valued.

##### MSC:
 39B82 Stability, separation, extension, and related topics for functional equations 39B52 Functional equations for functions with more general domains and/or ranges
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