Jordan σ-derivations of triangular algebras

We consider the problem of describing the form Jordan sigma-derivations of a triangular algebra A. The main result states that every Jordan sigma-derivation Delta of A is of the form Delta = d + delta, where d is a sigma-derivation of A and delta is a special mapping of A. We search for sufficient conditions on a triangular algebra, such that delta = 0. In particular, any Jordan sigma-derivation of a nest algebra T (N) is a sigma-derivation and any Jordan sigma-derivation of an upper triangular matrix algebra T-n (A), where A is a commutative unital algebra, is a sigma-derivation.