The main purpose of this paper is to characterize some additive mappings satisfying certain functional equations in rings with involution. In particular, we prove that any Jordan *-centralizer on a 2-torsion free semiprime *-ring is a reverse *-centralizer. As an application of this result, Jordan *-centralizers of semiprime rings are characterized. Further, we establish that if R is a (m + n)!- torsion free noncommutative prime ring with involution * and D, G are Jordan *-derivations on R such that D(x~m)x~n ± x~nG(x~m) = 0 for all x e R, where m, n are non-negative integers, then D = G = 0. This result is in the spirit of the classical result of Posner [21], which states that: Let R be a prime ring and D a derivation of R such that xD(x) - D(x)x = 0 for all x ∈ R. Then R is commutative or D = 0.
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