On the \(q\)-Bernstein polynomials of unbounded functions with \(q > 1\)

DOI10.1155/2013/349156zbMath1279.41015OpenAlexW2007651274WikidataQ58916002 ScholiaQ58916002MaRDI QIDQ369884

Sofiya Ostrovska, Ahmet Yaşar Özban

Publication date: 19 September 2013

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

Full work available at URL: https://doi.org/10.1155/2013/349156

zbMATH Keywords

\(q\)-Bernstein polynomialsunbounded functions

Mathematics Subject Classification ID

Approximation by polynomials (41A10) Algorithms for approximation of functions (65D15)

Related Items (5)

The \(q\)-versions of the Bernstein operator: from mere analogies to further developments ⋮ The \(q\)-Bernstein polynomials of the Cauchy kernel with a pole on \([0,1\) in the case \(q>1\)] ⋮ Evaluation of norm of \((p,q)\)-Bernstein operators ⋮ On the \(q\)-Bernstein polynomials of rational functions with real poles ⋮ The convergence of \((p,q)\)-Bernstein operators for the Cauchy kernel with a pole via divided difference

Cites Work

• The moments for \(q\)-Bernstein operators in the case \(0<q<1\)
• The \(q\)-Bernstein basis as a \(q\)-binomial distribution
• The saturation of convergence on the interval [0,1 for the \(q\)-Bernstein polynomials in the case \(q>1\)]
• Asymptotics of the roots of Bernstein polynomials used in the construction of modified Daubechies wavelets.
• The norm estimates of the \(q\)-Bernstein operators for varying \(q>1\)
• Properties of convergence for \(\omega,q\)-Bernstein polynomials
• The approximation of power function by the q-Bernstein polynomials in the case qϡ1
• The q-deformed binomial distribution and its asymptotic behaviour
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