Abstract
Let R be a semiprime ring with involution * and let F, D : R -> R be additive mappings satisfying the conditions (i) F(x(2)) = F(x)x* + x* D(x) and D(x(2)) = D(x)x*+ x* D(x); (ii) F(x(n+1)) = F(x)(x*)(n) + x* D(x)(x*)(n-1) +(x*)(2) D(x)(x*)(n-2) + . . . + (x*)(n) D(x) for all x is an element of R. Then, F(xy) = F(y) x*+ y* D(x) and D(xy) = D(y)x*+ y* D(x) for all x, y is an element of R.