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

Abstract

In this paper, we define a generalized additive set-valued functional equation, which is related to the following generalized additive functional equation: f(x(1) + ... + x(l)) = (l-1)f(x(1) + ... + x(l-1)/l-1) + 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.