On (θ, θ)-Derivations in Semiprime Rings

The main objective of the present paper is to prove the following result: let m and n be positive integers with m+n not equal to 0, and let R be an (m+n+2)!- torsion free semiprime ring with identity element. Let θ be an automorphism of R. Suppose there exists an additive mapping D:R→R such that D(x^(m+n+1))= (m+n+1) θ (x^m) D(x) θ (x^n) for all xϵR, then D is a (θ, θ)-derivation on R.