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 equations\begin{align*} 2\varphi(x + y) + \varphi(x - y) &= 3\varphi(x)+ 3\varphi(y) \\ 2\psi(x + y) + \psi(x - y) &= 3\psi(x) + 2\psi(y) + \psi(-y).\end{align*}We also consider the Pexider type functional equation \[2\psi(x + y) + \psi(x - y) = f(x) + g(y),\] and the additive functional equation\[2\psi(x + y) + \psi(x - y) = 3\psi(x) + \psi(y).\]

Keywords

• hyers-ulam stability
• additive
• quadratic
• drygas
• functional equation
• lebesgue measure zero
• pexider equation