Additive mappings covering generalized (alpha_1, alpha_2)-derivations in semiprime rings

Abstract

Let R be a semiprime ring, (α1,α2) be automorphisms on R and Δ, δ be additive maps from R to R. If Δ and δ satisfying any one of the following identities:i) Δ(xnyn)=Δ(xn)α1(yn)+α2(xn)δ(yn)ii) Δ(xn)=Δ(xn-m)α1(xm)+α2(xn-m)δ(xm), for all x,y∈Rthen Δ will be generalized (α1,α2)-derivation with associated (α1,α2)-derivation on R.