Stability of an additive-quadratic-quartic functional equation

In this paper, we investigate the stability of an additive-quadratic-quartic functional equation$$\begin{align*}f(x+2y)& +f(x-2y)-2f(x+y)-2f(-x- y)-2f(x-y)-2f(y-x)\nonumber \\ &+4f(-x)+ 2f(x)-f(2y)-f(-2y)+4f(y)+4f(-y)=0 \end{align*}$$by the direct method in the sense of Găvruta.