The stability of Cauchy equations in the space of Schwartz distributions

We reformulate the stability theorem of D.H. Hyers in the Schwartz tempered distributions and prove that every -additive tempered distribution can be approximated by a linear function. We also consider the superstability of the Cauchy equation f (x +y) = f (x)f (y).  2004 Elsevier Inc. All rights reserved.