A note on approximation properties of \(q\)-Durrmeyer operators

DOI10.1016/j.amc.2010.01.086zbMath1188.41015OpenAlexW2075960094MaRDI QIDQ969149

Xiao-Ming Zeng, Diwang Lin, Ling-Ling Li

Publication date: 11 May 2010

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

Full work available at URL: https://doi.org/10.1016/j.amc.2010.01.086

zbMATH Keywords

continuous functions\(q\)-Durrmeyer operators\(q\)-Bernstein polynomialspositive linear operatorsapproximation process

Mathematics Subject Classification ID

Approximation by operators (in particular, by integral operators) (41A35) Simultaneous approximation (41A28)

Related Items (7)

On generalized integral Bernstein operators based on \(q\)-integers ⋮ A survey of results on the limit \(q\)-Bernstein operator ⋮ The \(q\)-Bernstein polynomials of the Cauchy kernel with a pole on \([0,1\) in the case \(q>1\)] ⋮ On the \(q\)-Bernstein polynomials of piecewise linear functions in the case \(q>1\) ⋮ Stancu type generalization of modified Schurer operators based on \(q\)-integers ⋮ On the sets of convergence for sequences of the \(q\)-Bernstein polynomials with \(q > 1\) ⋮ Approximation properties for the genuine modified Bernstein-Durrmeyer-Stancu operators

Cites Work

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• Convergence of generalized Bernstein polynomials
• On the improvement of analytic properties under the limit \(q\)-Bernstein operator
• Voronovskaya-type formulas and saturation of convergence for \(q\)-Bernstein polynomials for \(0 < q < 1\)
• Sur l'approximation de fonctions intégrables sur l'interval-0,1-ferme par des polynômes de Bernstein modifies
• Interpolation and approximation by polynomials
• Saturation of convergence for \(q\)-Bernstein polynomials in the case \(q\geqslant 1\)
• \(q\)-Bernstein polynomials of the Cauchy kernel
• Properties of convergence for \(\omega,q\)-Bernstein polynomials
• Some approximation properties of \(q\)-Durrmeyer operators
• Quantum calculus

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