Solutions and the Generalized Hyers-Ulam-Rassias Stability of a Generalized Quadratic-Additive Functional Equation

Abstract

We study general solutions and generalized Hyers-Ulam-Rassias stability of the following $n$-dimensional functional equation $f\left({{\displaystyle \sum }}_{i=1}^k{x}_i\right)+(k-2){{\displaystyle \sum }}_{i=1}^{k}f\left(x_i\right)={{\displaystyle \sum }}_{i=1}^k{{\displaystyle \sum }}_{j=1,j>i}^{k}f(x_i+x_j)$, $k\ge 3$, on non-Archimedean normed spaces.