Abstract
Let R be any (n+1)I-torsion free ring and F,D : R -> R be additive mappings satisfying F(x(n+1)) = (alpha(x))(n) F (x) = Sigma(n)(i=1) (alpha(x)(n-i)(beta(x))D-i(x) for all x is an element of R, where n is a fixed integer and alpha, beta are automorphisms of R. Then, D is Jordan left (alpha, beta)-derivation and F is generalized Jordan left (alpha,beta)-derivation on R and if additive mappings F and D is Jordan (alpha, beta)-derivation and F is generalized Jordan (alpha, beta)-derivation on R.At last some Immediate consequence of the above theorems have been given.