Direct and Converse Results on Weighted Simultaneous Approximation by the Method of Operators of Baskakov-Durrmeyer Type

We consider the n- th. operators of Baskakov-Durrmeyer type, which result from the classical Baskakov-type operators with weights p _nk, if the values f(k/n) are replaced by the integral terms ((n - c)int_{I} p_{nk} (t) f(t) dt ) , where I denotes the corresponding interval which depends on the parameter c. For integrable functions the rate of weighted simultaneous approximation will be related to the Ditzian-Totik modulus of smoothness.