二次函数方程在广义函数空间上的Ulam型稳定性

Ulam Stability of Quadratic Functional Equation in the Space of Distributions

通过在缓增广义函数空间上重新定义二次函数方程的Ulam型稳定性,利用广义函数正则化方法,证明了二次函数方程Hyers-Ulam-Rassias型函数方程的稳定性,并给出了缓增广义函数当满足Ulam型二次函数方程不等式时与二次函数的接近程度.

We reformulated the Ulam＇ s stability of quadratic functional equation in the space of tempered distributions and made use of regularization method to prove the Hyers-Ulam-Rassias stability of quadratic functional equation in the space of tempered distributions, giving the degree of approximation between quadratic function and the tempered distribution which satisfies Ulam＇ s quadratic functional inequality.