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Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 939565, 6 pages
http://dx.doi.org/10.1155/2013/939565
Research Article

Estimation of Approximation with Jacobi Weights by Multivariate Baskakov Operator

School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received 7 May 2013; Accepted 14 July 2013

Academic Editor: Yongsheng S. Han

Copyright © 2013 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

We first give the unboundedness of multivariate Baskakov operators with the normal weighted norm. By introducing new norms, using the multivariate decomposition technique and the modulus of smoothness with Jacobi weight, the upper bound estimation of multivariate Baskakov operators is obtained. The obtained results not only generalize the corresponding ones for multivariate Baskakov operators without weights, but also give the approximation accuracy with the Jacobi weights approximation.