ON GENERALIZED SKEW-COMMUTING MAPPINGS OF PRIME RINGS

Let R be a ring. Two mappings f : R -> R and g : R -> R are said to be generalized skew-commuting on R if f (x) g(x) + g( x) f (x) = 0 for all x in R. The main purpose of this paper is to prove the following result, which generalizes the conjecture of Nadeem et al.: Let R be a 2-torsion free prime ring with g : R -> R a non-zero isomorphism or anti-isomorphism of R. If f and g are generalized skew-commuting on R, then f (x) = 0 for all x in R.