Year: 2012
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.