On the eigenvectors of the q -Bernstein operators

DOI10.1002/mma.2814zbMath1291.41002OpenAlexW2033216050MaRDI QIDQ5406966

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Publication date: 4 April 2014

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.2814

zbMATH Keywords

eigenvalueseigenvectors\(q\)-integers\(q\)-binomial coefficients\(q\)-Bernstein operator

Mathematics Subject Classification ID

Eigenvalue problems for linear operators (47A75) Linear operators on function spaces (general) (47B38) Approximation by polynomials (41A10) Approximation by positive operators (41A36)

Related Items (6)

The \(q\)-versions of the Bernstein operator: from mere analogies to further developments ⋮ On the Eigenstructure of the Modified Bernstein Operators ⋮ Structure properties for binomial operators ⋮ On the eigenstructure of the $q$-Durrmeyer operators ⋮ On the eigenstructure of the $(\alpha,q)$-Bernstein operator ⋮ On the eigenfunctions of the \(q\)-Bernstein operators

Cites Work

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• Convergence of generalized Bernstein polynomials
• The \(q\)-Bernstein basis as a \(q\)-binomial distribution
• The saturation of convergence on the interval [0,1 for the \(q\)-Bernstein polynomials in the case \(q>1\)]
• \(q\)-Bernstein polynomials and their iterates.
• The eigenstructure of the Bernstein operator
• Asymptotics of the roots of Bernstein polynomials used in the construction of modified Daubechies wavelets.
• The diagonalisation of the multivariate Bernstein operator
• Saturation of convergence for \(q\)-Bernstein polynomials in the case \(q\geqslant 1\)
• Iterates of Bernstein polynomials
• Higher order limit q-Bernstein operators
• The norm estimates for the $q$-Bernstein operator in the case $q>1$
• Convexity and generalized Bernstein polynomials
• The q-deformed binomial distribution and its asymptotic behaviour

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