We introduce a new type of generalized derivations associate with Hochschild 2-cocycles and prove that every generalized Jordan derivation of this type is a generalized derivation under certain conditions. This result contains the results of I. N. Herstein [6, Theorem 3.1] and M. Ashraf and N-U. Rehman [1, Theorem].
NAKAJIMA, ATSUSHI (2006) "Note on Generalized Jordan Derivations Associate with Hochschild 2-cocycles of Rings," Turkish Journal of Mathematics: Vol. 30: No. 4, Article 5. Available at: https://journals.tubitak.gov.tr/math/vol30/iss4/5