Yilmaz, Ovgu GurelOstrovska, SofiyaTuran, MehmetMathematics2024-07-052024-07-0520240420-12132391-466110.1515/dema-2023-01572-s2.0-85192013288https://doi.org/10.1515/dema-2023-0157https://hdl.handle.net/20.500.14411/2239This study deals with the one-parameter family {D-q}(q is an element of[0,1]) of Bernstein-type operators introduced by Gupta and called the limit q-Durrmeyer operators. The continuity of this family with respect to the parameter q is examined in two most important topologies of the operator theory, namely, the strong and uniform operator topologies. It is proved that {D-q}(q is an element of[0,1]) is continuous in the strong operator topology for all q is an element of [0, 1]. When it comes to the uniform operator topology, the continuity is preserved solely at q = 0 and fails at all q is an element of (0, 1]. In addition, a few estimates for the distance between two limit q-Durrmeyer operators have been derived in the operator norm on C[0, 1].eninfo:eu-repo/semantics/closedAccessq-Durrmeyer operatorq-Bernstein operatoroperator normstrong operator topologyuniform operator topologyArticleQ1571WOS:0012079324000010