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The generalized Hyers–Ulam–Rassias stability of a cubic functional equation. (English) Zbl 1021.39014
The authors consider the functional equation \[ f(2x+y) +f(2x-y)=2f(x+y)+ 2f(x-y)+12f(x). \] They determine the general solution, which is of the form \(f(x)= B(x,x,x)\) where \(B\) is symmetric and additive in each variable. Moreover they investigate the stability properties of this equation.
Reviewer: J.Schwaiger (Graz)

MSC:
39B82 Stability, separation, extension, and related topics for functional equations
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