Turkish Journal of Mathematics, cilt.47, sa.6, ss.1643-1658, 2023 (SCI-Expanded)
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.