Hyers-Ulam stability of a generalized additive set-valued functional equation

n this paper, we define a generalized additive set-valued functional equation, which is related to the following generalized additive functional equation $$ f(x_1 + \cdots + x_l) = (l-1)f\left( \frac{x_1 + \cdots + x_{l-1}} {l-1}\right) + f(x_l)$$ for a fixed integer $l$ with $l>1$, and prove the Hyers-Ulam stability of the generalized additive set-valued functional equation.