This is an announcement for the paper "Korovkin type theorem for iterates of certain positive linear operators" by Nazim I. Mahmudov.
Abstract: In this paper we prove that if T:C[0,1]→C[0,1] is a positive linear operator with T(e₀)=1 and T(e₁)-e₁ does not change the sign, then the iterates T^{m} converges to some positive linear operator T^{∞} :C[0,1]→C[0,1] and we derive quantitative estimates in terms of modulii of smoothness. This result enlarges the class of operators for which the limit of the iterates can be computed and the quantitative estimates of iterates can be given.
Archive classification: math.FA
Submitted from: mahmudov2009@gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.2918
or