APPROXIMATE (rho, tau)-CONTRACTIBILITY

Abstract

In this paper, the generalized Hyers-Ulam{Rassias stability of (rho, tau)-derivations on normed algebras into Banach bimodules is established. The Cauchy{Rassias inequality is used. This inequality was introduced for the ¯rst time by Th. M. Rassias in his paper entitled: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. We introduce the notion of approximate (rho, tau)-contractibility and prove that a Banach algebra is (rho, tau)-contractible if and only if it is approximately (rho, tau)-contractible.