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On the continuity in q of the family of the limit q-Durrmeyer operators

Yılmaz Övgü Gürel, Ostrovska Sofiya, Turan Mehmet

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20230157

This study deals with the one-parameter family […] 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 […] 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].