The cubic $\rho$-functional equation in matrix non-Archimedean random normed spaces

Abstract

Using the direct method and the fixed point method, we investigate the Hyers-Ulam stability of the following cubic-$\rho$ functional equation
\begin{align*}
f(x&+2y)+f(x-2y)-2f(x+y)-2f(x-y)-12f(x)\nonumber \\
&=\rho{\bigg(4f(x+\frac{y}{2})+4f(x-\frac{y}{2})-f(x+y)-f(x-y)-6f(x)\bigg)}
\end{align*}
in matrix non-Archimedean random normed spaces, where $\rho$ is a fixed real number with $\rho\neq 2$.