On the eigenstructure of the $q$-Durrmeyer operators

Authors: ÖVGÜ GÜREL YILMAZ

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.

Keywords: $q$-integers, $q$-Stirling numbers, $q$-Bernstein-Durrmeyer operators, moments, eigenvalues, eigenfunctions

Full Text: PDF