论文部分内容阅读
Let G be an Abelian group and letρ:G×G→[0,∞) be a metric on G. Let E be a normed space. We prove that under some conditions if f:G→E is an odd function and Cx:G→E defined by Cx(y):=2 f (x+y)+2 f (x?y)+12 f (x)?f (2x+y)?f (2x?y) is a cubic function for all x∈G, then there exists a cubic function C:G→E such that f?C is Lipschitz. Moreover, we investigate the stability of cubic functional equation 2 f (x+y)+2 f (x?y)+12 f (x)?f (2x+y)?f (2x?y)=0 on Lipschitz spaces.