A note on generalized (; )-derivations in Banach algebras

Let A be a Banach algebra , and are linear mappings (or homomorphisms) on Banach algebra A. A linear map d : A ! A is called ( ; )-derivation if d(ab) = d(a) (b) + (a)d(b) a; b 2 A . A linear mapping : A ! A is called a ( ; )-derivation if there exists a ( ; )- derivation d : A ! A such that (ab) = (a) (b) + (a)d(b) (a; b 2 A): In this talk, we investigate automatic continuity of these derivations on Banach algebras.

Keywords:

Banach algebra , Generalized derivation , Generalized inner derivation.