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International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 94136, 11 pages

Linear operators that preserve some test functions

Faculty of Mathematics and Computer Science, BabeĊŸ-Bolyai University, Cluj-Napoca 400084, Romania

Received 6 October 2005; Revised 23 March 2006; Accepted 4 April 2006

Copyright © 2006 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper centers around a pair of sequences of linear positive operators. The former has the degree of exactness one and the latter has its degree of exactness null, but, as a novelty, it reproduces the third test function of Korovkin theorem. Quantitative estimates of the rate of convergence are given in different function spaces traveling from classical approximation to approximation in abstract spaces. Particular classes are also studied.