Korovkin type theorem and iterates of certain positive linear operators
Functional Analysis
2010-12-07 v1
Abstract
In this paper we prove Korovkin type theorem for iterates of general positive linear operators and derive quantitative estimates in terms of modulus of smoothness. In particular, we show that under some natural conditions the iterates converges strongly to a fixed point of the original operator . The results can be applied to several well-known operators; we present here the -MKZ operators, the -Stancu operators, the genuine -Bernstein--Durrmeyer operators and the Cesaro operators.
Cite
@article{arxiv.1012.1187,
title = {Korovkin type theorem and iterates of certain positive linear operators},
author = {N. I. Mahmudov},
journal= {arXiv preprint arXiv:1012.1187},
year = {2010}
}