Some identities for the operator of Bleimann, Butzer and Hahn involving divided differences

Abstract:

The paper introduces a set of identities involving divided differences and linear operators. On their basis, some of the best known properties of, and a set of new results on, the operator of Bleimann, Butzer and Hahn, can be obtained easily from the corresponding properties of Bernstein operators. Among several other results, a Stancu-type form for the remainder of the Bleimann, Butzer and Hahn approximation process is obtained. Furthermore, we study simultaneous approximation, preservation of convexity of higher order for the operator of Bleimann, Butzer and Hahn and obtain new saturation and inverse theorems.