On the Stability of a Parametric Additive Functional Equation in Quasi-Banach Spaces

Abstract

We investigate the generalized Hyers-Ulam stability of the following functional equation ${\sum }_{i=1}^{m}f(x_i)=1/2m\left[{\sum }_{i=1}^{m}f\left(m{x}_i+{\sum }_{j=1,j\ne i}^m{x}_j\right)+f\left({\sum }_{i=1}^m{x}_i\right)\right]$ for a fixed positive integer $m$ with $m\ge 2$ in quasi-Banach spaces.