Hyers-Ulam-Rassias Stability Of Functional Equation In The Space Of Tempered Distributions

In this paper we consider the stability theorems of the Jensen equation and Jensen-Pexider equation in the spaces S′of Schwartz tempered distributions.Making use of pullback we reformulate two inequalities of functions in the space S′(Rⁿ) of Schwartz tempered distributions. Using mollifier to convert inequality to smooth function inequality in space of Rⁿ⁺¹ ,we solve the stability of smooth function,then by the relation between regularizing function and generalize distribution,we have the stability of Jensen function and Jensen-Pexider function.