可加函数方程在广义函数空间上的稳定性

Stability of an additive functional equation in the space of generalized functions

利用广义函数正则化的方法给出1个可加函数在广义函数空间上的一般解,并且利用热方程的核给出该函数方程在缓增广义函数上的Hyers-Ulam-Rassias型稳定性,进一步推广了文献[1]的结论.

We investigate the general solution of an additive functional equation in the space of generalized functions using the method of regularizing distributions,and give the Hyers-Ulam-Rassias stability of an additive functional equation in the space of tempered distributions using heat kernel.Our results generalize the reference of [1].