Stability of Mixed Additive–Quadratic and Additive–Drygas Functional Equations

Abstract

In this paper, using the Baire category theorem we investigate the Hyers–Ulam stability problem of mixed additive–quadratic and additive–Drygas functional equations $$\begin{aligned} 2f(x+y) + f(x-y) - 3f(x) -3f(y)&= 0,\\ 2f(x+y) + f(x-y) - 3f(x) -2f(y) -f(-y)&= 0 \end{aligned}$$on a set of Lebesgue measure zero. As a consequence, we obtain asymptotic behaviors of the functional equations.