Turan, MehmetYilmaz, Ovgu GurelOstrovska, SofiyaOstrovska, SofiyaTuran, MehmetMathematics2024-07-052024-07-05202401617-94472195-372410.1007/s40315-024-00534-72-s2.0-85189642170https://doi.org/10.1007/s40315-024-00534-7https://hdl.handle.net/20.500.14411/2242The limit q-Durrmeyer operator, D-infinity,D-q, was introduced and its approximation properties were investigated by Gupta (Appl. Math. Comput. 197(1):172-178, 2008) during a study of q-analogues for the Bernstein-Durrmeyer operator. In the present work, this operator is investigated from a different perspective. More precisely, the growth estimates are derived for the entire functions comprising the range of D-infinity,D-q. The interrelation between the analytic properties of a function f and the rate of growth for D(infinity,q)f are established, and the sharpness of the obtained results are demonstrated.eninfo:eu-repo/semantics/openAccessq-Durrmeyer operatorAnalytic functionEntire functionGrowth estimatesArticleQ1Q2WOS:001198572900001