Abstract
We consder the n-th so-called operators of Baskakov-Durrmeyer type, which result from the classical Baskakov-type operators with weights pnk, if the discrete values f(k/n) are replaced by the integral terms (n-c∫ ∞0 p n k(t)f(t)dt. The main differences between these operators and their classical and Kantorovicvariants 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 smootheness of a function we use the Ditzian-Totik modulus of smoothness and its equivalence to appropriate K-functionals.
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This paper is part of the author's dissertation.
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Heilmann, M. Direct and converse results for operators of Baskakov-Durrmeyer type. Approx. Theory & its Appl. 5, 105–127 (1989). https://doi.org/10.1007/BF02836120
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DOI: https://doi.org/10.1007/BF02836120