Smoothness properties of positive summation integral operators


In this paper we are dealing with approximation by summation integral operatos. We show the connections between the local smoothness of the approximated function and the rate of its local approximation. The direct theorem is obtained in a general case. Also, an inverse result is presented under certain conditions imposed on the sequence of operators, the most important being the commutativity of the operators and a restriction on the second order moments of the operators.


Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


Durrmeyer operator; Lipschitz continuity; rate of convergence; Korovkin theorem

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O. Agratini, Smoothness properties of positive summation integral operators, East Journal on Approximation, 5 (1999) no. 4, pp. 381-392.


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East Journal on approximation

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Publisher DARBA (Bulgaria)

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