The convergence of \(q\)-Bernstein polynomials \((0< q< 1)\) and limit \(q\)-Bernstein operators in complex domains

DOI10.1216/RMJ-2009-39-4-1279zbMath1173.41304OpenAlexW2064399544MaRDI QIDQ2270587

Sofiya Ostrovska, He Ping Wang

Publication date: 28 July 2009

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmj-2009-39-4-1279

zbMATH Keywords

uniform convergence\(q\)-integers

Mathematics Subject Classification ID

Approximation by polynomials (41A10) Approximation by operators (in particular, by integral operators) (41A35)

Related Items (1)

A survey of results on the limit \(q\)-Bernstein operator

Cites Work

• 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 \(0 < q < 1\)
• \(q\)-Bernstein polynomials and their iterates.
• Korovkin-type theorem and application
• Interpolation and approximation by polynomials
• The approximation by \(q\)-Bernstein polynomials in the case \(q \downarrow 1\)
• The rate of convergence of \(q\)-Bernstein polynomials for \(0<q<1\)
• Properties of convergence for the \(q\)-Meyer-König and Zeller operators
• The convergence ofq-Bernstein polynomials (0 <q< 1) in the complex plane
• Generalized Bernstein polynomials
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