A Note on Jordan Triple Higher -Derivations on Semiprime Rings

We introduce the following notion. Let ℕ0 be the set of all nonnegative integers and let D=(di)i∈ℕ0 be a family of additive mappings of a *-ring R such that d0=idR; D is called a Jordan higher *-derivation (resp., a Jordan higher *-derivation) of R if dn(x2)=∑i+j=n‍di(x)dj(x*i) (resp., dn(xyx)=∑i+j+k=n‍di(x)dj(y*i)dk(x*i+j)) for all x,y∈R and each n∈ℕ0. It is shown that the notions of Jordan higher *-derivations and Jordan triple higher *-derivations on a 6-torsion free semiprime *-ring are coincident.