On the eigenstructure of the q -Durrmeyer operators

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Yilmaz Ö.

Turkish Journal of Mathematics, vol.47, no.6, pp.1643-1658, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 6
  • Publication Date: 2023
  • Doi Number: 10.55730/1300-0098.3454
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1643-1658
  • Keywords: eigenfunctions, eigenvalues, moments, q -Bernstein-Durrmeyer operators, q -integers, q -Stirling numbers
  • Recep Tayyip Erdoğan University Affiliated: Yes


The purpose of this paper is to establish the eigenvalues and the eigenfunctions of both the q -Durrmeyer operators Dn,q and the limit q -Durrmeyer operators D∞,q introduced by V. Gupta in the case 0 < q < 1. All moments for Dn,q and D∞,q are provided. The coefficients for the eigenfunctions of the operators are explicitly derived and the eigenfunctions of these operators are illustrated by graphical examples.