Abstract
Let R be a prime ring of characteristic not 2, U a nonzero square closed Lie ideal of R and F, G, H be the generalized derivations with associated derivations d, delta, h of R respectively. In the present paper, we study the situations if one the follwoing holds ( 1) F(u)G(v) +/- H(uv) is an element of Z(R), (2) F(u) F(v) +/- H(vu) is an element of Z(R), for all u, v is an element of U, then U subset of Z(R).