Let G be a dividing group, the Hyers-Ulam stability of the following general functional equation 1/nf(x) +1/mf(y) +f(z)=f(x/n+y/m+z),(V)x,y,z ∈ G,m,n ∈ Z+ ,m,n ≠ 1 is investigated and obtained by using the improved Rassias direct method.%考察了泛函方程1/n(x)+1/mf(y)+f(z)=f(x/n+y/m+z),(V)x,y,z∈G 的Hyers-Ulam稳定性,其中m,n∈Z+,m,n≠1.改进了Rassias方法,并使用改进后的Rassias方法得到这个泛函方程的广义Hyers-Ulam稳定性.
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