On the eigenstructure of the q-Durrmeyer operators
TURKISH JOURNAL OF MATHEMATICS, vol.47, no.6, 2023 (SCI-Expanded, Scopus)
- 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
- Keywords: eigenfunctions, eigenvalues, moments, q -Bernstein-Durrmeyer operators, q -integers, q -Stirling numbers
- Recep Tayyip Erdoğan University Affiliated: Yes
Abstract
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.