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Volume 5, Issue 3
The Simultaneous Approximation Average Errors for Bernstein Operators on the $r$-Fold Integrated Wiener Space

Guiqiao Xu

DOI: 10.4208/nmtma.2012.m11006

Numer. Math. Theor. Meth. Appl., 5 (2012), pp. 403-422.

Published online: 2012-05

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  • Abstract

For weighted approximation in $L_p$ -norm, we determine strongly asymptotic orders for the average errors of both function approximation and derivative approximation by the Bernstein operators sequence on the $r$-fold integrated Wiener space.

  • Keywords

Bernstein operators, weighted $L_p$-norm, r-fold integrated Wiener space, average error.

  • AMS Subject Headings

41A28, 65D05, 41A25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-5-403, author = {Guiqiao Xu}, title = {The Simultaneous Approximation Average Errors for Bernstein Operators on the $r$-Fold Integrated Wiener Space}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2012}, volume = {5}, number = {3}, pages = {403--422}, abstract = {

For weighted approximation in $L_p$ -norm, we determine strongly asymptotic orders for the average errors of both function approximation and derivative approximation by the Bernstein operators sequence on the $r$-fold integrated Wiener space.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2012.m11006}, url = {http://global-sci.org/intro/article_detail/nmtma/5944.html} }
TY - JOUR T1 - The Simultaneous Approximation Average Errors for Bernstein Operators on the $r$-Fold Integrated Wiener Space AU - Guiqiao Xu JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 403 EP - 422 PY - 2012 DA - 2012/05 SN - 5 DO - http://doi.org/10.4208/nmtma.2012.m11006 UR - https://global-sci.org/intro/article_detail/nmtma/5944.html KW - Bernstein operators, weighted $L_p$-norm, r-fold integrated Wiener space, average error. AB -

For weighted approximation in $L_p$ -norm, we determine strongly asymptotic orders for the average errors of both function approximation and derivative approximation by the Bernstein operators sequence on the $r$-fold integrated Wiener space.

Guiqiao Xu. (2012). The Simultaneous Approximation Average Errors for Bernstein Operators on the $r$-Fold Integrated Wiener Space. Numerical Mathematics: Theory, Methods and Applications. 5 (3). 403-422. doi:10.4208/nmtma.2012.m11006
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