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Approximation of bounded continuous functions by linear combinations of Phillips operators

Tachev G.

Demonstratio Mathematica

2014

Vol. 47, nr 3

662--671

We study the approximation properties of linear combinations of the so-called Phillips operators, which can be considered as genuine Szász–Mirakjan–Durrmeyer operators. As main result, we prove a direct estimate for the rate of approximation of bounded continuous functions (…), measured in (…)-norm and thus generalizing the results, proved earlier by Gupta, Agrawal, and Gairola in [3]. Our estimates rely on the recent results, obtained in the joint works of M. Heilmann and the author [10, 11].