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We prove a general stability theorem of an  n -dimensional quadratic-additive type functional equation    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\begin{aligned} Df(x_1, x_2, \ldots , x_n) = \sum _{i=1}^m c_i f \big ( a_{i1}x_1 + a_{i2}x_2 + \cdots + a_{in}x_n \big ) = 0 \end{aligned}$$\end{document}D  f   (   x  1   ,   x  2   ,  …  ,   x  n   )   =   ∑   i  =  1   m    c  i   f   (    a   i  1x  1   +   a   i  2x  2   +  ⋯  +   a   i  nx  n    )   =  0by applying the direct method.

A general theorem on the stability of a class of functional equations including quadratic-additive functional equations