A distributional version of functional equations and their stabilities

Generalizing the results in [J. Math. Anal. Appl. 286 (2003) 177-186; J. Math. Anal. Appl. 295 (2004) 107-114; Arch. Math., to appear; J. Math. Anal. Appl. 299 (2004) 578-586] that consider the Hyers-Ulam stability problems of several functional equations in the spaces of the Schwartz tempered distributions and the Fourier hyperfunctions we consider the stability problems of the functional equations in the space of distributions.