Weighted approximation by multidimensional Bernstein operators
The purpose of this paper is to give inverse theorems for univariate and multivariate Bernstein operators with some Jacobi weights. The main result in the univariate case is an analogue of the inverse theorem for weighted approximation by Kantorovich operators proved by \textit{Z. Ditzian} and \textit{V. Totik}, Moduli of smoothness (1987; Zbl 0666.41001). In the multivariate case few inverse results are known. The first result of this kind was obtained by \textit{Z. Ditzian}, Inverse theorems for multidimensional Bernstein operators, Pac. J. Math. 121, 293-319 (1986; Zbl 0581.41023)]. Here the author discusses the weighted approximation problem for multidimensional Bernstein operators.
scientific article; zbMATH DE number 575577