On the eigenfunctions of the \(q\)-Bernstein operators

DOI10.1007/S43034-022-00235-ZOpenAlexW4309580837MaRDI QIDQ2105344

Mehmet Turan, Sofiya Ostrovska

Publication date: 8 December 2022

Published in: Annals of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s43034-022-00235-z

zbMATH Keywords

eigenvalueeigenfunctioninfinite linear system\(q\)-Bernstein operator

Mathematics Subject Classification ID

Eigenvalue problems for linear operators (47A75) Approximation by positive operators (41A36)

Uses Software

• MathOverflow

Cites Work

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• The \(q\)-versions of the Bernstein operator: from mere analogies to further developments
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• The \(q\)-Bernstein basis as a \(q\)-binomial distribution
• The eigenstructure of the Bernstein operator
• The diagonalisation of the multivariate Bernstein operator
• Some approximation properties of \(q\)-Durrmeyer operators
• Discrete q-Distributions
• Quantum deformations andq-boson operators
• Bernstein Operators and Their Properties
• On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)_q
• The q-deformed boson realisation of the quantum group SU(n)_qand its representations
• The quantum group SU_q(2) and a q-analogue of the boson operators
• The rate of convergence ofq-Durrmeyer operators for 0<q<1
• Convexity and generalized Bernstein polynomials
• The q-deformed binomial distribution and its asymptotic behaviour
• A survey of results on the q-Bernstein polynomials
• Beta operators with Jacobi weights
• On the eigenvectors of the q -Bernstein operators

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