Volume 34, Issue 1
On Weighted $L^p$-Approximation by Weighted Bernstein-Durrmeyer Operators

Anal. Theory Appl., 34 (2018), pp. 1-16.

Published online: 2018-07

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• Abstract

In the present paper, we establish direct and converse theorems for weighted Bernstein-Durrmeyer operators under weighted $L^p$−norm with Jacobi weight $w(x) = x^{\alpha}(1−x)^{\beta}$. All the results involved have no restriction $\alpha$, $\beta<1-\frac{1}{p}$, which indicates that the weighted Bernstein-Durrmeyer operators have some better approximation properties than the usual Bernstein-Durrmeyer operators.

• Keywords

Weighted $L^p$−approximation, weighted Bernstein-Durrmeyer operators, direct and converse theorems.

41A10, 41A25

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@Article{ATA-34-1, author = {}, title = {On Weighted $L^p$-Approximation by Weighted Bernstein-Durrmeyer Operators}, journal = {Analysis in Theory and Applications}, year = {2018}, volume = {34}, number = {1}, pages = {1--16}, abstract = {

In the present paper, we establish direct and converse theorems for weighted Bernstein-Durrmeyer operators under weighted $L^p$−norm with Jacobi weight $w(x) = x^{\alpha}(1−x)^{\beta}$. All the results involved have no restriction $\alpha$, $\beta<1-\frac{1}{p}$, which indicates that the weighted Bernstein-Durrmeyer operators have some better approximation properties than the usual Bernstein-Durrmeyer operators.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2018.v34.n1.1}, url = {http://global-sci.org/intro/article_detail/ata/12541.html} }
TY - JOUR T1 - On Weighted $L^p$-Approximation by Weighted Bernstein-Durrmeyer Operators JO - Analysis in Theory and Applications VL - 1 SP - 1 EP - 16 PY - 2018 DA - 2018/07 SN - 34 DO - http://doi.org/10.4208/ata.2018.v34.n1.1 UR - https://global-sci.org/intro/article_detail/ata/12541.html KW - Weighted $L^p$−approximation, weighted Bernstein-Durrmeyer operators, direct and converse theorems. AB -

In the present paper, we establish direct and converse theorems for weighted Bernstein-Durrmeyer operators under weighted $L^p$−norm with Jacobi weight $w(x) = x^{\alpha}(1−x)^{\beta}$. All the results involved have no restriction $\alpha$, $\beta<1-\frac{1}{p}$, which indicates that the weighted Bernstein-Durrmeyer operators have some better approximation properties than the usual Bernstein-Durrmeyer operators.

Meiling Wang, Dansheng Yu & Dejun Zhao. (1970). On Weighted $L^p$-Approximation by Weighted Bernstein-Durrmeyer Operators. Analysis in Theory and Applications. 34 (1). 1-16. doi:10.4208/ata.2018.v34.n1.1
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