On the rate of convergence for the \(q\)-Durrmeyer polynomials in complex domains (Q6634079)

In the year 2008 the \(q\)-Durrmeyer operators were introduced (see [\textit{V. Gupta}, Appl. Math. Comput. 197, No. 1, 172--178 (2008; Zbl 1142.41008)]). Such operators are one of the popular \(q\)-versions of the classical operators in approximation theory. The present article deals with the study on the approximation properties in complex domain of these operators. It is proved that the rate of convergence on a compact set \(D \subset C\) for these operators is of order \(O(q^n)\) as \(n\to \infty\), where \(0<q<1.\)