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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.

MSC:
39B82Stability, separation, extension, and related topics
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References:
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