Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 7 1 2016 01 01 Approximately generalized additive functions in several variables via fixed point method 167 181 304 10.22075/ijnaa.2015.304 EN R. Farokhzad Rostami Department of Mathematics, Gonbad Kavous University, Gonbad Kavous, Golestan, Iran S.A.R. Hoseinioun Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701, USA Journal Article 2014 08 14 In this paper, we obtain the general solution and the generalized   Hyers-Ulam-Rassias stability in random normed spaces, in non-Archimedean spaces and also in $p$-Banach spaces and finally the stability via fixed point method for a functional equation<br />\begin{align*}<br />&D_f(x_{1},.., x_{m}):= \sum^{m}_{k=2}(\sum^{k}_{i_{1}=2}<br />\sum^{k+1}_{i_{2}=i_{1}+1}... \sum^{m}_{i_{m-k+1}=i_{m-k}+1})<br /> f(\sum^{m}_{i=1, i\neq i_{1},...,i_{m-k+1} }<br /> x_{i}-\sum^{m-k+1}_{ r=1} x_{i_{r}})\\& \hspace {2.8cm}+f(\sum^{m}_{ i=1} x_{i})<br />-2^{m-1} f(x_{1})=0<br />\end{align*}<br />where $m \geq 2$ is an integer number. Additive function $p$-Banach spaces Random normed spaces Non-Archimedean spaces Fixed point method generalized Hyers-Ulam stability https://ijnaa.semnan.ac.ir/article_304_9d50c3cecad33f485b18a635d7221af3.pdf