Yong-Soo Jung and Kyoo-Hong Park Sun Moon University, Seowon University
Abstract : Let $\mathcal A$ be a Banach algebra and let $f:\mathcal A\times\mathcal A\to\mathcal A$ be an approximate bi-derivation in the sense of Hyers-Ulam-Rassias. In this note, we proves the Hyers-Ulam-Rassias stability of bi-derivations on Banach algebras. If, in addition, $\mathcal A$ is unital, then $f:\mathcal A\times\mathcal A\to\mathcal A$ is an exact bi-derivation. Moreover, if $\mathcal A$ is unital, prime and $f$ is symmetric, then $f=0$.