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

In this paper, using the Baire category theorem we investigate the Hyers–Ulam stability problem of mixed additive–quadratic and additive–Drygas functional equations 2f(x+y)+f(x-y)-3f(x)-3f(y)=0,2f(x+y)+f(x-y)-3f(x)-2f(y)-f(-y)=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} 2f(x+y) + f(x-y) - 3f(x) -3f(y)&= 0,\\ 2f(x+y) + f(x-y) - 3f(x) -2f(y) -f(-y)&= 0 \end{aligned}$$\end{document}on a set of Lebesgue measure zero. As a consequence, we obtain asymptotic behaviors of the functional equations.