On the generalized Hyers-Ulam-Rassias stability of a quadratic functional equation

摘要

In this paper, we investigate the generalized Hyers-Ulam-Rassias stability of a quadratic functional equation $f(x+y+z)+f(x-y)+f(y-z)+f(z-x)=3f(x)+3f(y)+3f(z)$ and prove the Hyers-Ulam-Rassias stability of the equation on bounded domain.