Korovkin type theorem and iterates of certain positive linear operators

2010/12/06 by Mahmudov, N. I.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1012.1187

Abstract

In this paper we prove Korovkin type theorem for iterates of general positive linear operators T:C[ 0,1] → C[ 0,1] and derive quantitative estimates in terms of modulus of smoothness. In particular, we show that under some natural conditions the iterates T^m:C[ 0,1] → C[ 0,1] converges strongly to a fixed point of the original operator T. The results can be applied to several well-known operators; we present here the q-MKZ operators, the q-Stancu operators, the genuine q-Bernstein--Durrmeyer operators and the Cesaro operators.

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