Approximately generalized additive functions in several variables via fixed point method

In this paper, we obtain the general solution and the generalized Hyers--Ulam--Rassias stability in random normed spaces, in non-Archimedean spacesand also in $p$-Banach spaces and finally the stability via fixed point method for a functional equation\begin{align*}&D_f(x_{1},.., x_{m}):= \sum^{m}_{k=2}(\sum^{k}_{i_{1}=2}\sum^{k+1}_{i_{2}=i_{1}+1}... \sum^{m}_{i_{m-k+1}=i_{m-k}+1}) f(\sum^{m}_{i=1, i\neq i_{1},...,i_{m-k+1}} x_{i}-\sum^{m-k+1}_{r=1} x_{i_{r}})\\& \hspace {2.8cm}+f(\sum^{m}_{i=1} x_{i})-2^{m-1} f(x_{1})=0\end{align*}where $m \geq 2$ is an integer number.