ON APPROXIMATION TO DISCRETE Q-DERIVATIVES OF FUNCTIONS VIA Q-BERNSTEIN-SCHURER OPERATORS

In the present paper, we shall investigate the pointwise approximation properties of the qanalogue of the Bernstein-Schurer operators and estimate the rate of pointwise convergence of these operators to the functions f whose qderivatives are bounded variation on the interval [0, 1 + p]: We give an estimate for the rate of convergence of the operator (B(n,p,q)f) at those points x at which the one sided qderivatives D-q(+) f (x) and D-q(-) f (x) exist. We shall also prove that the operators (B(n,p,q)f) (x) converge to the limit f (x). As a continuation of the very recent and initial study of the author deals with the pointwise approximation of the qBernstein Durrmeyer operators [12] at those points x at which the one sided qderivatives D-q(+) f (x) and D-q(-) f(x) exist, this study provides (or presents) a forward work on the approximation of q -analogue of the Schurer type operators in the space of DqBV