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 $b$-Generalized derivations on Banach algebras Commun. Korean Math. Soc.Published online July 20, 2021 Husain Alhazmi 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. MSC numbers : 16W25, 46J10 Full-Text :