Some results on *-differential identities in prime rings

Let R be a prime ring with involution * of the second kind. An additive mapping F : R -> R is called generalized derivation if there exists a unique derivation d such that F(xy) = F(x)y + xd(y) for all x,y is an element of R. In this paper, we investigate the structure of R and describe the possible forms of generalized derivations of R that satisfy specific *-differential identities. Precisely, we study the following situations: (i) F(x) omicron G(x*) = 0, (ii) F(x) omicron x* = x omicron G(x*), (iii) F(x omicron x*) = G(x) omicron G(x*), (iv) F(x) omicron G(x*) = x omicron x* for all x is an element of R. Moreover, we construct some examples showing that the restrictions imposed in the hypotheses of our theorems are not redundant.