Korovkin type theorem for iterates of certain positive linear operators

Details Korovkin type theorem for iterates of certain positive linear operators Korovkin type theorem for iterates of certain positive linear operators

2011-03-15

arxiv.org/abs/1103.2918v1

Mathematics

Functional Analysis

Scientific paper

In this paper we prove that if T:C[0,1] \rightarrow C[0,1] is a positive linear operator with T(e_0)=1 and T(e_1)-e_1 does not change the sign, then the iterates T^{m} converges to some positive linear operator T^{\infty} :C[0,1] \rightarrow 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.

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