Bulletin of the
Korean Mathematical Society BKMS

In this paper, we will find out the general solution and investigate the generalized Hyers--Ulam--Rassias stability problem for the following cubic functional equation \begin{equation*} 3f(x+3y)+f(3x-y)=15f(x+y)+15f(x-y)+80f(y). \end{equation*} The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. {\bf 72} (1978), 297--300.

Keywords: Hyers--Ulam--Rassias stability, cubic functional equation

MSC numbers: Primary 39B52, 46L05, 47B48