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

Abstract

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}Df(x1,x2,…,xn)=∑i=1mcif(ai1x1+ai2x2+⋯+ainxn)=0by applying the direct method.