Asymptotic behavior of a generalized functional equation

In this paper, we investigate the Hyers-Ulam stability problem of the following functional equation

$$f(x+y)+g(x-y)=h(x)+k(y),$$

on an unbounded restricted domain, which generalizes some of the results already obtained by other authors (for example [9,Theorem 2], [11,Theorem 5] and [21,Theorem 2]). Particular cases of this functional equation are Cauchy, Jensen, quadratic and Drygas functional equations. As a consequence, we obtain asymptotic behaviors of this functional equation.