(untitled) (Analysis in Theory and Applications, 2014)
Let G be an Abelian group and let ρ:G × G → [0, ∞) be a metric on G. Let ε be a normed space. We prove that under some conditions if f:G→ε is an odd function and C_x:G→ε defined by C_x(y):=2f(x+y)+2f(x-y)+12f(x)- f(2x+y)-f(2x-y) is a cubic function for all xG, then there exists a cubic function C:G→ε such that f-C is Lipschitz. Moreover, we investigate the stability of cubic functional equation 2f(x+y)+2f(x-y)+12f(x)-f(2x+y) -f(2x-y)=0 on Lipschitz spaces.