Heilmann, M. Direct and converse results for operators of Baskakov-Durrmeyer type. (English) Zbl 0669.41014 Approximation Theory Appl. 5, No. 1, 105-127 (1989). We consider the nth so-called operators of Baskakov-Durrmeyer type, which result from the classical Baskakov-type operators with weights \(p_{nk}\), if the discrete values f(k/n) are replaced by the integral terms \((n-c)\int^{\infty}_{0}p_{nk}(t)f(t)dt.\) The main difference between these operators and their classical and Kantorovich-variants respectively is that they commute. We prove direct and converse theorems also for linear combinations of the operators and results of Zamansky- Sunouchi type. As an important tool for measuring the smoothness of a function we use the Ditzian-Totik modulus of smoothness and its equivalence to appropriate K-functionals. Cited in 3 ReviewsCited in 37 Documents MSC: 41A36 Approximation by positive operators Keywords:operators of Baskakov-Durrmeyer type; weights; Ditzian-Totik modulus of smoothness; K-functionals PDFBibTeX XMLCite \textit{M. Heilmann}, Approximation Theory Appl. 5, No. 1, 105--127 (1989; Zbl 0669.41014)