Volume 28, Issue 2
Convergence of Derivatives of Generalized Bernstein Operators

Anal. Theory Appl., 28 (2012), pp. 135-145.

Published online: 2012-06

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• Abstract

In the present paper, we obtain estimations of convergence rate derivatives of the $q$-Bernstein polynomials $B_n(f,q_n;x)$ approximating to $f'(x)$ as $n\to\infty$ which is a generalization of that relating the classical case $q_n = 1$. On the other hand, we study the convergence properties of derivatives of the limit $q$-Bernstein operators $B_\infty( f,q;x)$ as $q\to 1^−.$

• Keywords

limit $q$-Bernstein operators, derivative of $q$-Bernstein polynomial, convergence, rate.

41A10, 41A25, 41A36

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@Article{ATA-28-135, author = { and L. Y. Zhu and and 21660 and and L. Y. Zhu and L. and Qiu and and 21661 and and L. Qiu}, title = {Convergence of Derivatives of Generalized Bernstein Operators}, journal = {Analysis in Theory and Applications}, year = {2012}, volume = {28}, number = {2}, pages = {135--145}, abstract = {

In the present paper, we obtain estimations of convergence rate derivatives of the $q$-Bernstein polynomials $B_n(f,q_n;x)$ approximating to $f'(x)$ as $n\to\infty$ which is a generalization of that relating the classical case $q_n = 1$. On the other hand, we study the convergence properties of derivatives of the limit $q$-Bernstein operators $B_\infty( f,q;x)$ as $q\to 1^−.$

}, issn = {1573-8175}, doi = {https://doi.org/10.3969/j.issn.1672-4070.2012.02.004}, url = {http://global-sci.org/intro/article_detail/ata/4550.html} }
TY - JOUR T1 - Convergence of Derivatives of Generalized Bernstein Operators AU - L. Y. Zhu , AU - Qiu , L. JO - Analysis in Theory and Applications VL - 2 SP - 135 EP - 145 PY - 2012 DA - 2012/06 SN - 28 DO - http://doi.org/10.3969/j.issn.1672-4070.2012.02.004 UR - https://global-sci.org/intro/article_detail/ata/4550.html KW - limit $q$-Bernstein operators, derivative of $q$-Bernstein polynomial, convergence, rate. AB -

In the present paper, we obtain estimations of convergence rate derivatives of the $q$-Bernstein polynomials $B_n(f,q_n;x)$ approximating to $f'(x)$ as $n\to\infty$ which is a generalization of that relating the classical case $q_n = 1$. On the other hand, we study the convergence properties of derivatives of the limit $q$-Bernstein operators $B_\infty( f,q;x)$ as $q\to 1^−.$

L. Y. Zhu & L. Qiu. (1970). Convergence of Derivatives of Generalized Bernstein Operators. Analysis in Theory and Applications. 28 (2). 135-145. doi:10.3969/j.issn.1672-4070.2012.02.004
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