Abstract
In this manuscript, we discuss the behaviour and nature of generalized derivation \({\mathscr {G}}\) on a (semi-) prime ring \({\mathscr {R}}\) satisfying certain differential identities over \({\mathscr {I}}\), a nonzero ideal of \({\mathscr {R}}\). Moreover, we extend our purely ring theoretic result to a non-commutative Banach algebras and obtained some range inclusion results of continuous generalized derivations.
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