Copyright © 2011 Jianjun Wang et al. This is an open access article distributed under the
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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