Using the equivalence relation between -functional and modulus of smoothness, we establish a strong direct theorem and an inverse theorem of weak type for multivariate Bernstein-Durrmeyer operators with Jacobi weights on a simplex in this paper. We also obtain a characterization for multivariate Bernstein-Durrmeyer operators with Jacobi weights on a simplex. The obtained results not only generalize the corresponding ones for Bernstein-Durrmeyer operators, but also give approximation order of Bernstein-Durrmeyer operators.
Jianjun Wang. Chan-Yun Yang. Shukai Duan. "Approximation Order for Multivariate Durrmeyer Operators with Jacobi Weights." Abstr. Appl. Anal. 2011 1 - 12, 2011. https://doi.org/10.1155/2011/970659