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

DOI10.1155/2013/159720zbMath1268.81094OpenAlexW2012726354WikidataQ59001908 ScholiaQ59001908MaRDI QIDQ2375419

Sofiya Ostrovska

Publication date: 14 June 2013

Published in: Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/159720

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Coherent states (81R30) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10)

Related Items (3)

The inversion results for the limit \(q\)-Bernstein operator ⋮ Approximating \(B\)-continuous functions using GBS operators of Bernstein-Schurer-Stancu type based on \(q\)-integers ⋮ The distance between two limit \(q\)-Bernstein operators

Cites Work

• Functions whose smoothness is not improved under the limit \(q\)-Bernstein operator
• A note on \(q\)-Bernstein polynomials
• \(q\)-Bernstein polynomials associated with \(q\)-Stirling numbers and Carlitz's \(q\)-Bernoulli numbers
• Some identities on the \(q\)-integral representation of the product of several \(q\)-Bernstein-type polynomials
• Convergence of generalized Bernstein polynomials
• On the improvement of analytic properties under the limit \(q\)-Bernstein operator
• \(q\)-parametric Bleimann Butzer and Hahn operators
• A note on approximation properties of \(q\)-Durrmeyer operators
• The \(q\)-Bernstein basis as a \(q\)-binomial distribution
• Korovkin-type theorems and applications
• \(q\)-Bernstein polynomials and their iterates.
• Korovkin-type theorem and application
• Interpolation and approximation by polynomials
• The functional-analytic properties of the limit \(q\)-Bernstein operator
• The convergence of \(q\)-Bernstein polynomials \((0< q< 1)\) and limit \(q\)-Bernstein operators in complex domains
• Positive linear operators generated by analytic functions
• Properties of convergence for \(\omega,q\)-Bernstein polynomials
• On the Lupaş \(q\)-analogue of the Bernstein operator
• Properties of convergence for the \(q\)-Meyer-König and Zeller operators
• Higher order limit q-Bernstein operators
• On the properties of the limit q-Bernstein operator
• On the image of the limitq-Bernstein operator
• The q-deformed boson realisation of the quantum group SU(n)_qand its representations
• The rate of convergence ofq-Durrmeyer operators for 0<q<1
• The q-deformed binomial distribution and its asymptotic behaviour
• Convergence properties of the q-deformed binomial distribution
• Quantum calculus
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