On the stability of a generalized cubic functional equation
Bull. Korean Math. Soc. 2008 Vol. 45, No. 4, 739-748 Printed December 1, 2008
Heejeong Koh and DongSeung Kang Dankook University
Abstract : In this paper, we obtain the general solution of a generalized cubic functional equation, the Hyers-Ulam-Rassias stability, and the stability by using the alternative fixed point for a generalized cubic functional equation \begin{equation*}\begin{aligned} &\ 4f(\sum^{n-1}_{j=1}x_j + mx_n) + 4f(\sum^{n-1}_{j=1}x_j-mx_n) +m^2\sum^{n-1}_{j=1}f(2x_j)\\ =&\ 8f(\sum^{n-1}_{j=1}x_j)+4m^2\sum^{n-1}_{j=1}\Big(f(x_j+ x_n) + f(x_j -x_n)\Big) \end{aligned}\end{equation*} for a positive integer $m \geq 1.$
