@article{Yılmaz2026, 
author = {Mine Menekşe Yılmaz and Erkan Agyuz},
title = {Szász–Durrmeyer-type operators generated by Euler polynomials of negative order via a Poisson–Gamma representation},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {19217-19241},
keywords = {Szász–Durrmeyer operators, Euler polynomials of negative order, positive linear operators, Poisson–Gamma representation, weighted Korovkin theorem, Voronovskaya theorem},
url = {https://www.sciopen.com/article/10.3934/math.2026782},
doi = {10.3934/math.2026782},
abstract = {We introduced a Szász–Durrmeyer-type family of positive linear operators generated by Euler polynomials of negative order    −  k, where    k  ∈      N  . The corresponding discrete kernel admits a finite binomial mixture of shifted Poisson probabilities, while the Durrmeyer integral part is described by a Gamma-type kernel. This Poisson–Gamma structure makes positivity and normalization transparent and provides a convenient basis for the computation of algebraic and central moments. Using these moments, we established quantitative estimates, weighted Korovkin-type convergence, and a compact-uniform Voronovskaya-type theorem. The asymptotic formula shows that the classical approximation order is preserved, whereas the negative-order Euler parameter affects only the drift term in the first-order asymptotic profile.}
}