ON THE STABILITY OF BI-DERIVATIONS IN BANACH ALGEBRAS

Title & Authors
ON THE STABILITY OF BI-DERIVATIONS IN BANACH ALGEBRAS
Jung, Yong-Soo; Park, Kyoo-Hong;

Abstract
Let A be a Banach algebra and let f : $\small{A{\times}A{\rightarrow}A}$ 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, A is unital, then f : $\small{A{\times}A{\rightarrow}A}$ is an exact bi-derivation. Moreover, if A is unital, prime and f is symmetric, then f = 0.
Keywords
bi-derivation;approximate bi-derivation;stability;
Language
English
Cited by
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