Abstract
In this article, we define the following: Let N-0 be the set of all nonnegative integers and D = (d(i))(i is an element of N0) a family of additive mappings of a *-ring R such that d(0) = id(R). D is called a Jordan (alpha, beta)-higher *-derivation (resp. a Jordan triple (alpha, beta)-higher *-derivation) of R if d(n)(a(2)) = Sigma(i+j=n)d(i)(beta(j)(a)d(j)(alpha(i)(a*(i))) (resp. d(n)(aba) = Sigma(i+j+k=n)d(i)(beta(j+k)(a)d(j)(beta(k)(alpha(i)(b*(i)))d(k)(alpha(i+j)(a*(i+j))) for all a, b is an element of R and each n is an element of N-0. We show that the two notions of Jordan (alpha, beta)-higher *-derivation and Jordan triple (alpha, beta)-higher *-derivation on a 6-torsion free semiprime *-ring are equivalent.