Multidimensional approximation operators generated by Lebesgue–Stieltjes measures

A general class of sequences of multidimensional positive linear operators is defined and studied; it includes, in particular, sequences of multidimensional Berstein polynomials. The main asymptotic term is obtained in the remainder when derivatives of functions in certain classes are approximated by derivatives of the values of the operators on these functions.
Bibliography: 10 titles.