On the Stability of Mixed Additive--Quadratic and Additive--Drygas Functional Equations

Abstract

In this paper, we have improved some of the results in [C. Choi and B. Lee, Stability of Mixed Additive-Quadratic and Additive--Drygas Functional Equations. Results Math. 75 no. 1 (2020), Paper No. 38]. Indeed, we investigate the Hyers-Ulam stability problem of the following functional equationsbegin{align*} 2varphi(x + y) + varphi(x - y) &= 3varphi(x)+ 3varphi(y) \ 2psi(x + y) + psi(x - y) &= 3psi(x) + 2psi(y) + psi(-y).end{align*}We also consider the Pexider type functional equation [2psi(x + y) + psi(x - y) = f(x) + g(y),] and the additive functional equation[2psi(x + y) + psi(x - y) = 3psi(x) + psi(y).]