On the eigenstructure of the $q$-Durrmeyer operators

DOI10.55730/1300-0098.3454OpenAlexW4387164554MaRDI QIDQ6117905

Övgü Gürel Yilmaz

Publication date: 21 February 2024

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

Full work available at URL: https://doi.org/10.55730/1300-0098.3454

zbMATH Keywords

momentseigenvalueseigenfunctions\(q\)-integers\(q\)-Stirling numbers\(q\)-Bernstein-Durrmeyer operators

Mathematics Subject Classification ID

Eigenvalue problems for linear operators (47A75) Linear operators on function spaces (general) (47B38)

Cites Work

• The \(q\)-versions of the Bernstein operator: from mere analogies to further developments
• The eigenstructure of the Bernstein operator
• Interpolation and approximation by polynomials
• \(q\)-Bernstein polynomials and Bézier curves
• Papers of L.V. Kantorovich on Bernstein polynomials
• The eigenstructure of operators linking the Bernstein and the genuine Bernstein-Durrmeyer operators
• Some approximation properties of \(q\)-Durrmeyer operators
• The rate of convergence ofq-Durrmeyer operators for 0<q<1
• Convexity and generalized Bernstein polynomials
• Bernstein-Bézier Methods for the Computer-Aided Design of Free-Form Curves and Surfaces
• On the eigenvectors of the q -Bernstein operators
• On the eigenstructure of the $(\alpha,q)$-Bernstein operator
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