Young-Sun Cho, Ick-Soon Chang, Hark-Mahn Kim
Acta Mathematica Sinica. 2009, 25(10): 0-0.
Let $n \ge 2$ be an integer.
In this paper, we investigate the generalized Hyers-Ulam-Rassias stability problem for
the following functional equation
\begin{eqnarray*}
f\left(\sum_{j =1}^{n-1} x_j + 2 x_n \right) + f\left(\sum_{j =1}^{n-1} x_j - 2 x_n \right) +8\sum_{j =1}^{n-1} f(x_j ) \= 2f\left(\sum_{j =1}^{n-1} x_j \right) + 4 \sum_{j =1}^{n-1}[ f( x_j + x_n) + f( x_j - x_n)],
\end{eqnarray*}
which contains as solutions cubic, quadratic or additive mappings.