On the eigenstructure of the q-Durrmeyer operators

Yilmaz Ö.

TURKISH JOURNAL OF MATHEMATICS, cilt.47, sa.6, 2023 (SCI-Expanded, Scopus) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Sayı: 6
  • Basım Tarihi: 2023
  • Doi Numarası: 10.55730/1300-0098.3454
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Anahtar Kelimeler: eigenfunctions, eigenvalues, moments, q -Bernstein-Durrmeyer operators, q -integers, q -Stirling numbers
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

The purpose of this paper is to establish the eigenvalues and the eigenfunctions of both the q-Durrmeyer operators D-n,D-q and the limit q-Durrmeyer operators D-infinity,D-q introduced by V. Gupta in the case 0 < q < 1. All moments for D-n,D-q and D-infinity,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.