The norm estimates for the $q$-Bernstein operator in the case $q>1$

DOI10.1090/S0025-5718-09-02273-XzbMath1216.47013MaRDI QIDQ3584780

Sofiya Ostrovska, He Ping Wang

Publication date: 30 August 2010

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

zbMATH Keywords

operator norm\(q\)-integers\(q\)-Bernstein polynomials\(q\)-binomial coefficients\(q\)-Bernstein operatorstrong asymptotic order

Mathematics Subject Classification ID

Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Approximation by polynomials (41A10) Banach spaces of continuous, differentiable or analytic functions (46E15) Rate of growth of functions, orders of infinity, slowly varying functions (26A12) Inequalities for trigonometric functions and polynomials (26D05)

Related Items (7)

The \(q\)-versions of the Bernstein operator: from mere analogies to further developments ⋮ The norm estimates of the \(q\)-Bernstein operators for varying \(q>1\) ⋮ Approximation by \(q\)-Bernstein polynomials in the case \(q \rightarrow 1 +\) ⋮ On the \(q\)-Bernstein polynomials of piecewise linear functions in the case \(q>1\) ⋮ On the eigenvectors of the q -Bernstein operators ⋮ On the analyticity of functions approximated by their \(q\)-Bernstein polynomials when \(q > 1\) ⋮ On the eigenstructure of the $(\alpha,q)$-Bernstein operator

Cites Work

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• Convergence of generalized Bernstein polynomials
• Dual generalized Bernstein basis
• Voronovskaya-type formulas and saturation of convergence for \(q\)-Bernstein polynomials for \(0 < q < 1\)
• The approximation of logarithmic function by \(q\)-Bernstein polynomials in the case \(q >1\)
• The \(q\)-Bernstein basis as a \(q\)-binomial distribution
• Regularizability of inverse linear operators in Banach spaces with bases
• \(q\)-Bernstein polynomials and their iterates.
• On de Casteljau's algorithm
• Korovkin-type theorem and application
• Asymptotics of the roots of Bernstein polynomials used in the construction of modified Daubechies wavelets.
• A counterexample to the Bishop-Phelps theorem in complex spaces
• Saturation of convergence for \(q\)-Bernstein polynomials in the case \(q\geqslant 1\)
• The rate of convergence of \(q\)-Bernstein polynomials for \(0<q<1\)
• The q-deformed binomial distribution and its asymptotic behaviour

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