On Approximation of Some Mixed Functional Equations

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.  ۷۵  no. ۱ (۲۰۲۰), Paper No. ۳۸]. Indeed, we investigate the Hyers-Ulam stability problem of the following   functional equations\begin{align*}  ۲\varphi(x + y) + \varphi(x - y) &= ۳\varphi(x)+ ۳\varphi(y)  \\  ۲\psi(x + y) + \psi(x - y) &= ۳\psi(x) + ۲\psi(y) + \psi(-y).\end{align*}We also consider the Pexider type functional equation \[۲\psi(x + y) + \psi(x - y) = f(x) + g(y),\] and the additive functional equation\[۲\psi(x + y) + \psi(x - y) = ۳\psi(x) + \psi(y).\]

Keywords:

Hyers-Ulam stability , Additive , Quadratic , Drygas , Functional equation , Lebesgue measure zero , Pexider equation