Abstract and Applied Analysis
Volume 2011 (2011), Article ID 970659, 12 pages
doi:10.1155/2011/970659
Research Article

Approximation Order for Multivariate Durrmeyer Operators with Jacobi Weights

1School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
2Department of Mechanical Engineering, Technology and Science Institute of Northern Taiwan, No. 2 Xue-Yuan Road, Beitou, Taipei 112, Taiwan
3School of Electronics and Information Engineering, Southwest University, Chongqing 400715, China

Received 3 January 2011; Accepted 15 February 2011

Academic Editor: Pavel Drábek

Copyright © 2011 Jianjun Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.