ON THE STABILITY OF AN n-DIMENSIONAL FUNCTIONAL EQUATION ORIGINATING FROM QUADRATIC FORMS

Abstract

In this paper, we investigate the generalized Hyers-Ulam-Rassias stability of an $n$-dimensional functional equation \begin{equation*} f\Big(\sum_{i=1}^{n}x_i, \sum_{i=1}^{n}y_i\Big)+\!\sum_{1\le i \lt j\le n}f(x_i-x_j, y_i-y_j)=n\sum_{i=1}^{n}f(x_i, y_i), \,\,\, (n\ge2). \end{equation*}