Korovkin type theorem for iterates of certain positive linear operators

2011/03/15 by Nazım I. Mahmudov, Mahmudov, Nazim I.
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1103.2918

openalex publication_date 2011/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Korovkin-type theorem and application

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