Characterization of mixed triple derivations on incidence algebras

Let R be a 2-torsion free commutative unital ring and I(S, R) be the incidence algebra of a locally finite preordered set S. In the present paper, we show that if an R-linear map T: I(S, R) ? I(S, R) satisfies T([t ? u, v]) = [T(t) ? u, v] + [t ? T(u), v] + [t ? u, T(v)], for all t, u, v ? I(S, R), then T = ? + ?, where ?: I(S, R) ? I(S, R) is a derivation and ?: I(S, R) ? Z(I(S, R)) is an R-linear map.