摘要
Let n be a fixed integer, let R be an （n ＋ 1）!-torsion free semiprime ring with the identity element and let F ： R → R be an additive mapping satisfying the relation F（xn＋2） ∑＋n＋i=1xi-1F（x）2xn＋1-i -∑xnF（x）xn＋1-i for all x 6 R. In this case, we prove that F is of the form 2F（x） = D（x） ＋ ax ＋ xa for all x ∈ R, where D ： R → R is a derivation and a 6 R is some fixed element.
Let n be a fixed integer, let R be an （n ＋ 1）!-torsion free semiprime ring with the identity element and let F ： R → R be an additive mapping satisfying the relation F（xn＋2） ∑＋n＋i=1xi-1F（x）2xn＋1-i -∑xnF（x）xn＋1-i for all x 6 R. In this case, we prove that F is of the form 2F（x） = D（x） ＋ ax ＋ xa for all x ∈ R, where D ： R → R is a derivation and a 6 R is some fixed element.
