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Article On the continuity in q of the family of the limit q-Durrmeyer operators(Demonstratio Mathematica, 2024-04-25) Gürel Yılmaz, Övgü; Ostrovska, Sofiya; Turan, MehmetThe present paper deals with the one-parameter family {Dq}q∈[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 {Dq}q∈[0,1] is continuous in the strong operator topology for all q ∈ [0, 1]. When it comes to the uniform operator topology, the continuity is preserved solely at q = 0, and fails at all q ∈ (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].