Abstract
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.
Authors
Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Keywords
Durrmeyer operator; Lipschitz continuity; rate of convergence; Korovkin theorem
Paper coordinates
O. Agratini, Smoothness properties of positive summation integral operators, East Journal on Approximation, 5 (1999) no. 4, pp. 381-392.
About this paper
Journal
East Journal on approximation
Publisher Name
Publisher DARBA (Bulgaria)
DOI
Print ISSN
1310-6236
Online ISSN
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