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

• Autores: Elena E. Berdysheva
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 149, Nº 2, 2007, págs. 131-150
• Idioma: inglés
• DOI: 10.1016/j.jat.2007.04.009
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• Resumen

  • We prove that the kernels of the Baskakov-Durrmeyer and the Szász-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.