Turkish Journal of Mathematics
Abstract
The purpose of this paper is to establish the eigenvalues and the eigenfunctions of both the $q$-Durrmeyer operators $D_{n,q}$ and the limit $q$-Durrmeyer operators $D_{\infty,q}$ introduced by V. Gupta in the case 0<$q$<1. All moments for $D_{n,q}$ and $D_{\infty,q}$ are provided. The coefficients for the eigenfunctions of the operators are explicitly derived and the eigenfunctions of these operators are illustrated by graphical examples.
DOI
10.55730/1300-0098.3454
Keywords
$q$-integers, $q$-Stirling numbers, $q$-Bernstein-Durrmeyer operators, moments, eigenvalues, eigenfunctions
First Page
1643
Last Page
1658
Recommended Citation
YILMAZ, Ö. G (2023). On the eigenstructure of the $q$-Durrmeyer operators. Turkish Journal of Mathematics 47 (6): 1643-1658. https://doi.org/10.55730/1300-0098.3454
