International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 94136, 11 pages
doi:10.1155/IJMMS/2006/94136
Linear operators that preserve some test functions
Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca 400084, Romania
Received 6 October 2005; Revised 23 March 2006; Accepted 4 April 2006
Copyright © 2006 Octavian Agratini. 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.
Abstract
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.