## Stability of a generalized mixed type additive, quadratic, cubic and quartic functional equation.(English)Zbl 1195.39010

The authors investigate the Hyers-Ulam-Aoki-Rassias stability of the following functional equation: $\begin{split} f(x+ay)+f(x-ay)=a^2[f(x+y)+f(x-y)]+2(1-a^2)f(x)+\\ +\frac{a^4-a^2}{12}[f(2y)+f(-2y)-4f(y)-4f(-y)].\end{split}$

### 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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