For $m=1,2,3,4$, we study the following set-valued functional equation \begin{equation*} f(ax+y)\oplus f(ax-y)=a^{m-2}[f(x+y)\oplus f(x-y)]\oplus 2(a^2-1)\big[a^{m-2}f(x)\oplus \frac{(m-2)(1-(m-2)^2)}{6}f(y)\big] \end{equation*} where $a$ is a fixed positive integer with $a>1$. We also prove the stability of this setvalued functional equation by using the Banach fixed point theorem.
