On the analyticity of functions approximated by their \(q\)-Bernstein polynomials when \(q > 1\)

DOI10.1016/j.amc.2010.04.020zbMath1204.30026OpenAlexW2062504940MaRDI QIDQ708133

Sofiya Ostrovska, Iossif V. Ostrovskii

Publication date: 11 October 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.04.020

zbMATH Keywords

uniform convergenceanalytic continuation\(q\)-integers\(q\)-Bernstein polynomials

Mathematics Subject Classification ID

Approximation in the complex plane (30E10)

Related Items (1)

The \(q\)-versions of the Bernstein operator: from mere analogies to further developments

Cites Work

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• On the approximation of analytic functions by the \(q\)-Bernstein polynomials in the case \(q>1\)
• Convergence of generalized Bernstein polynomials
• The saturation of convergence on the interval [0,1 for the \(q\)-Bernstein polynomials in the case \(q>1\)]
• A generalization of the Bernstein polynomials
• \(q\)-Bernstein polynomials and their iterates.
• The eigenstructure of the Bernstein operator
• Korovkin-type theorem and application
• Asymptotics of the roots of Bernstein polynomials used in the construction of modified Daubechies wavelets.
• \(q\)-Bernstein polynomials of the Cauchy kernel
• On genuine Bernstein-Durrmeyer operators
• A Markov-type inequality for arbitrary plane continua
• The approximation of power function by the q-Bernstein polynomials in the case qϡ1
• The norm estimates for the $q$-Bernstein operator in the case $q>1$
• Simultaneous approximation by Bernstein-Sikkema operators
• Random Bernstein Polynomials

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