Let R be a prime ring of characteristic different from two with the sec- ond involution ∗ and α an automorphism of R . An additive mapping F of R is called a generalized ( α,α )-derivation on R if there exists an ( α,α )-derivation d of R such that F ( xy )= F ( x ) α ( y )+ α ( x ) d ( y ) holds for all x,y∈R. The paper deals with the s- tudy of some commutativity criteria for prime rings with involution. Precisely, we describe the structure of R admitting a generalized ( α,α )-derivation F satisfying any one of the following properties:
( i ) F ( xx^∗) −α ( xx^∗) ∈Z ( R ).
( ii ) F ( xx^∗ )+ α ( xx^∗ ) ∈Z ( R ).
( iii ) F ( x ) F ( xx^∗) −α ( xx^∗) ∈Z ( R ).
( iv ) F ( x ) F (x^∗)+ α ( xx^∗) ∈Z ( R ).
( v ) F ( xx^∗) −F ( x ) F (x^∗ ) ∈Z ( R ).
( vi ) F ( xx^∗) −F (x^∗) F ( x )=0
for all x∈R . Also, some examples are given to demonstrate that the restriction of the various results is not superfluous. In fact, our results unify and extend several well known theorems in literature.