On certain \(q\)-Durrmeyer type operators (Q1008609)

Replacing in the definition of the Durrmeyer operator binomials by \(q\)-binomials, \(q\in\mathbb{N}\setminus\{1\}\), the authors extend to this case the known approximation results for the Bernstein polynomials. Here the \(q\)-binomial \({n\choose k}_q\) is \({(n!)_q\over (k!)_q((n-k))_q}\), where \((n!)_q:= \prod^n_{k=0} {1-q^k\over 1-q}\).