Bulletin of the
Korean Mathematical Society BKMS

In this paper, we investigate the generalized Hyers占Ulam--Rassias stability of the following additive functional equation \[ 2\sum_{j =1}^{n}f\Big( \frac{x_{j}}{2} + \sum_{i =1 , i\neq j}^{n}x_{i}\Big)+ \sum_{j =1}^{n}f(x_{j}) = 2n f\big(\sum_{j =1}^{n}x_{j}\big), \] in quasi-$\beta$-normed spaces.

Keywords: generalized Hyers-Ulam stability, contractively subadditive, expansively superadditive, quasi-$\beta$-normed space, $(\beta,p)$-Banach space

MSC numbers: Primary 39B72, 39B82, 46B03, 47Jxx