Abstract
We construct the Stancu-type generalization of q-Bernstein operators involving the idea of Bezier bases depending on the shape parameter -1 <= zeta <= 1 and obtain auxiliary lemmas. We discuss the local approximation results in term of a Lipschitz-type function based on two parameters and a Lipschitz-type maximal function, as well as other related results for our newly constructed operators. Moreover, we determine the rate of convergence of our operators by means of Peetre's K-functional and corresponding modulus of continuity.