Approximation by \(q\)-Bernstein polynomials in the case \(q \rightarrow 1 +\)

DOI10.1155/2014/259491zbMath1470.41007OpenAlexW2034679619WikidataQ59037091 ScholiaQ59037091MaRDI QIDQ1722474

Xuezhi Wu

Publication date: 14 February 2019

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2014/259491

Mathematics Subject Classification ID

Approximation by polynomials (41A10) Approximation by positive operators (41A36)

Cites Work

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• Convergence of generalized Bernstein polynomials
• Voronovskaya-type formulas and saturation of convergence for \(q\)-Bernstein polynomials for \(0 < q < 1\)
• The approximation of all continuous functions on [0, 1 by \(q\) -Bernstein polynomials in the case \(q \rightarrow 1^{+}\)]
• The saturation of convergence on the interval [0,1 for the \(q\)-Bernstein polynomials in the case \(q>1\)]
• \(q\)-Bernstein polynomials and their iterates.
• Korovkin-type theorem and application
• Saturation of convergence for \(q\)-Bernstein polynomials in the case \(q\geqslant 1\)
• The norm estimates of the \(q\)-Bernstein operators for varying \(q>1\)
• The approximation by \(q\)-Bernstein polynomials in the case \(q \downarrow 1\)
• The rate of convergence of \(q\)-Bernstein polynomials for \(0<q<1\)
• The norm estimates for the $q$-Bernstein operator in the case $q>1$
• Direct and converse results for q-Bernstein operators
• A generalization of the Bernstein polynomials based on the q-integers
• A survey of results on the q-Bernstein polynomials

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