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 $q\to 1^−.$