Some identities involving divided differences

To study approximation properties of linear positive operators various identities involving divided differences are used. The aim of this note is to present two types of such kind of identities. The first one was used by Abel and Ivan [Abel, U. and Ivan, M., Some identities for the operator of Bleimamm, Butzer and Hahn involving divided differences, Calcolo, 36 (1999), 143–160; Abel, U. and Ivan, M., New representation of the remainder in the Bernstein approximation, J. Math. Anal. Appl., 381 (2011), No. 2, 952–956] to derive approximation properties of Bleimann, Butzer and Hahn (BBH) operators from the corresponding properties of the classical Bernstein operators. The second type of identifies can be used to derive some approximation properties of the BBH operators from the properties of some Stancu type operators.