In this paper we prove the Hyers-Ulam-Rassias stability by considering the cases that the approximate remainder ${varphi}$ is defined by (x * y) ＋ (x * $y^{-1}$) - 2 (x) - 2 (y) =<${varphi}$(x,y), (x*y*z)＋ (x)＋ (y)＋ (z)－ (x*y)－ (y*z)－ (z*x)＝${varphi}$(x, y, z), where (G,*) is a group, X is a real or complex Hausdorff topological vector space, and is a function from G into X.