Let A be a Banach algebra and M be a Banach Abimodule. We say that a linear mapping  : A !Mis a generalized -derivation whenever there exists a -derivation d : A !M such that (ab) = (a)(b)+(a)d(b) for all a, b 2 A. Giving some facts concerning generalized -derivations, we prove that if A is unital and if  : A ! A is a generalized -derivation and there exists an element a 2 A such that d(a) is invertible then  is continuous if and only if d is continuous. We also show that if M is unital, has no zero divisor and  : A ! M is a generalized -derivation such that d(1) 6= 0 then ker() is a bi-ideal of A and ker() = ker() = ker(d), where 1 denotes the unit element of A.

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