Journal of Applied Mathematics
Volume 2012 (2012), Article ID 346132, 9 pages
http://dx.doi.org/10.1155/2012/346132
Research Article

Derivatives of Multivariate Bernstein Operators and Smoothness with Jacobi Weights

Jianjun Wang,1 Zuoxiang Peng,1 Shukai Duan,2 and Jia Jing1

1School of Mathematics and Statistics, Southwest University, Chongqing 400715, China
2School of Electronics and Information Engineering, Southwest University, Chongqing 400715, China

Received 19 October 2011; Accepted 27 December 2011

Academic Editor: George Jaiani

Copyright © 2012 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 modulus of smoothness, directional derivatives of multivariate Bernstein operators with weights are characterized. The obtained results partly generalize the corresponding ones for multivariate Bernstein operators without weights.