Studying Baskakov--Durrmeyer operators and quasi-interpolants via special functions

Authors:
Elena E. Berdysheva
Affiliations:
Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, D-70593 Stuttgart, Germany
Venue:
Journal of Approximation Theory
Year:
2007

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Abstract

We prove that the kernels of the Baskakov-Durrmeyer and the Szasz-Mirakjan-Durrmeyer operators are completely monotonic functions. We establish a Bernstein type inequality for these operators and apply the results to the quasi-interpolants recently introduced by Abel. For the Baskakov-Durrmeyer quasi-interpolants, we give a representation as linear combinations of the original Baskakov-Durrmeyer operators and prove an estimate of Jackson-Favard type and a direct theorem in terms of an appropriate K-functional.