Commun. Korean Math. Soc. Published online July 20, 2021
King Abdulaziz University, Jeddah, KSA
Abstract : In this paper, we show, among others, that if $A$ is a Banach algebra satisfying a functional identity involving $b$-generalized derivation $F$ on $A$, under some subsequent conditions, is of the form $F(x)=ax$ for all $x\in R$, where $a\in Q_r$, a right Martindale quotient ring of $A$.
Keywords : Banach algebra, $b$-generalized derivation, right Martindale quotient ring.