Convergence of Derivatives of Generalized Bernstein Operators

Convergence of Derivatives of Generalized Bernstein Operators

Year:    2012

Author:    L. Y. Zhu, L. Qiu

Analysis in Theory and Applications, Vol. 28 (2012), Iss. 2 : pp. 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 $q\to 1^−.$

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.3969/j.issn.1672-4070.2012.02.004

Analysis in Theory and Applications, Vol. 28 (2012), Iss. 2 : pp. 135–145

Published online:    2012-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    11

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

Author Details

L. Y. Zhu

L. Qiu