General solution and generalized Ulam-Hyers stability of a generalized 3-Dimensional AQCQ functional equation

Abstract

In this paper, we achieve the general solution and generalized Ulam-Hyers stability of a generalized 3dimensional AQCQ functional equation$$\begin{aligned}f(x+r(y+z))+f(x- & r(y+z))=r^2[f(x+y+z)+f(x-y-z)]+2\left(1-r^2\right) f(x) \\+ & \frac{\left(r^4-r^2\right)}{12}[f(2(y+z))+f(-2(y+z))-4 f(y+z)-4 f(-(y+z))]\end{aligned}$$for all positive integers $r$ with $r \geq 2$ in Banach Space using two different methods.