Abstract：In this paper， based on the approximation properties of the Stancu-type q-Bernstein-Durrmeyer operator obtained in real space， the definition of the q-Bernstein-Durrmeyer operator in complex space is given. Referring to the research method in Ref. [8]， the approximation properties of the q-Bernstein-Durrmeyer operator and the Stancu-type q-Bernstein-Durrmeyer operator in 1≤k≤n to the analytic function on the compact disk are studied， and the Voronovskaja type results are obtained.
2025, Vol. 59 
