Jordan higher all-derivable points in triangular algebras

Let T be a triangular algebra. We say that D={Dn:n∈N}⊆L(T) is a Jordan higher derivable mapping at G if Dn(ST+TS=∑i+j=nDi(S)Dj(T)+Di(T)Dj(S)) for any S,T∈T with ST=G. An element G∈T is called a Jordan higher all-derivable point of T if every Jordan higher derivable linear mapping D={Dn}n∈N at G is a higher derivation. In this paper, under some mild conditions on T, we prove that some elements of T are Jordan higher all-derivable points. This extends some results in [6] to the case of Jordan higher derivations.