Some properties of q-Bernstein-Durrmeyer operators

In the present paper we shall investigate the pointwise approximation properties of the q analogue of the Bernstein-Durrmeyer operators and estimate the rate of pointwise convergence of these operators to the functions f whose q-derivatives are bounded variation on the interval [0, 1]. We give an estimate for the rate of convergence of the operator (L-n, (q)f) at those points x at which the one sided q-derivatives D-q(+) f(x), D-q(-) f(x)exist. We shall also prove that the operators L-n, (q)f converges to the limit f (x). To the best of my knowledge, the present study will be the first study on the approximation of q- operators in the space of DqBV