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Approximation Order for Multivariate Durrmeyer Operators with Jacobi Weights

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  • Jianjun Wang
  • Chan-Yun Yang
  • Shukai Duan

Abstract

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.

Suggested Citation

  • Jianjun Wang & Chan-Yun Yang & Shukai Duan, 2011. "Approximation Order for Multivariate Durrmeyer Operators with Jacobi Weights," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-12, April.
    • Handle: RePEc:hin:jnlaaa:970659
    DOI: 10.1155/2011/970659
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