The \(q\)-Bernstein polynomials of the Cauchy kernel with a pole on \([0,1]\) in the case \(q>1\)

DOI10.1016/j.amc.2013.07.034zbMath1329.33026OpenAlexW1999152084MaRDI QIDQ902566

Sofiya Ostrovska, Ahmet Yaşar Özban

Publication date: 18 January 2016

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

Full work available at URL: https://doi.org/10.1016/j.amc.2013.07.034

zbMATH Keywords

convergenceCauchy kernel\(q\)-integers\(q\)-Bernstein polynomialsapproximation of unbounded functions

Mathematics Subject Classification ID

Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items (3)

Approximation of Discontinuous Functions by q-Bernstein Polynomials ⋮ 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

• On the \(q\)-Bernstein polynomials of unbounded functions with \(q > 1\)
• The moments for \(q\)-Bernstein operators in the case \(0<q<1\)
• A note on approximation properties of \(q\)-Durrmeyer operators
• On certain \(q\)-Durrmeyer type operators
• Approximation theorems for generalized complex Kantorovich-type operators
• Asymptotics of the roots of Bernstein polynomials used in the construction of modified Daubechies wavelets.
• \(q\)-Bernstein polynomials of the Cauchy kernel
• Properties of convergence for \(\omega,q\)-Bernstein polynomials
• Some approximation properties of \(q\)-Durrmeyer operators
• The rate of convergence ofq-Durrmeyer operators for 0<q<1
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