Asymptotic expansion of multivariate Kantorovich type operators (Q1776183)

The paper is devoted to the asymptotic study of simultaneous approximation by Kantorovich type operators in the multivariate case.The authors define a Kantorovich type modification of a linear operator.Applying some some earlier results [\textit{López-Moreno} et al, Appl. Math. 287--307 (2002; Zbl 1049.41018)] and [J. Comput. Appl. Math. 150, No. 2, 219--251 (2003; Zbl 1025.41013)] in the References ),they obtain asymptotic formulae for the Kantorovich modification of a linear operator using the expansion of the original operator. As applications,the Kantorovich modification of the Bernstein operators defined on a simplex and the Kantorovich modification of Bleiman,Butzer and Hahn operators defined on a simplex are presented.