Ostrovska, SofiyaTuran, Mehmet2026-02-052026-02-0520260021-90451096-043010.1016/j.jat.2025.1062802-s2.0-105025763734https://doi.org/10.1016/j.jat.2025.106280https://hdl.handle.net/20.500.14411/11111The focus of this work is on the properties of the q-Durrmeyer operators Mn,q, n E N, and M infinity,q introduced, for q E (0, 1), by V. Gupta and H. Wang. First, it is shown that, for each f E C[0, 1], the sequence {Mn,q f}nEN converges to M infinity,q f uniformly on [0, 1] with a rate not slower than Cq, fqn, which refines the previously available result by V. Gupta and H. Wang, and implies the possibility of an analytic continuation for M infinity,q f into a neighbourhood of [0, 1]. Further investigation shows that M infinity,q f admits an analytic continuation as an entire function regardless of f E C[0, 1]. Finally, the growth estimates for these functions are received and applied to describe the point spectrum of M infinity,q. The paper also addresses the significant differences between the properties of M infinity,q and the previously (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.eninfo:eu-repo/semantics/closedAccessQ-Durrmeyer OperatorQ-Bernstein OperatorAnalytic FunctionGrowth RatePoint SpectrumArticle