On the stability of bi-derivations in Banach algebras
Bull. Korean Math. Soc. 2011 Vol. 48, No. 5, 959-967
Printed September 1, 2011
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 $f=0$.
Keywords : bi-derivation, approximate bi-derivation, stability
MSC numbers : 39B72, 39B52
Downloads: Full-text PDF  

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd