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Solution and stability of a mixed type additive, quadratic, and cubic functional equation. (English) Zbl 1177.39031

Summary: We obtain the general solution and the generalized Hyers-Ulam-Rassias stability of the mixed type additive, quadratic, and cubic functional equation
\[ f(x+2y) - f(x - 2y)=2(f(x+y) - f(x - y))+2f(3y) - 6f(2y)+6f(y). \]

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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References:

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