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arXiv · 1502.07237

Approximation properties of the $q$-Bal\'{a}zs-Szabados operators in the case $q\geq1$

N. I. Mahmudov
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Abstract

This paper deals with approximation properties of the newly defined $q$-generalization of the Bal\'{a}zs-Szabados operators in the case $q\geq1$. Quantitative estimates of the convergence and Voronovskaja type theorem are given. In particular, it is proved that the rate of approximation by the $q$-Bal\'{a}zs-Szabados ($q>1$) is of order $q^{-n}$ versus $1/n$ for the classical Bal\'{a}zs-Szabados ($q=1$) operators. The results are new even for the classical case $q=1$.

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BibTeXRIS

N. I. Mahmudov. 2015-02-25. Approximation properties of the $q$-Bal\'{a}zs-Szabados operators in the case $q\geq1$. https://arxiv.org/abs/1502.07237

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