Approximation Order for Multivariate Durrmeyer Operators with Jacobi Weights

Abstract EN

Using the equivalence relation between K-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.