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Displaying similar documents to “Remarks on Voronovskaya's theorem.”

Bernstein type operators having 1 and x j as fixed points

Zoltán Finta (2013)

Open Mathematics

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For certain generalized Bernstein operators {L n} we show that there exist no i, j ∈ {1, 2, 3,…}, i < j, such that the functions e i(x) = x i and e j (x) = x j are preserved by L n for each n = 1, 2,… But there exist infinitely many e i such that e 0(x) = 1 and e j (x) = x j are its fixed points.

Simultaneous approximation by a class of Bernstein-Durrmeyer operators preserving linear functions

Heiner Gonska, Radu Păltănea (2010)

Czechoslovak Mathematical Journal

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We introduce and study a one-parameter class of positive linear operators constituting a link between the well-known operators of S. N. Bernstein and their genuine Bernstein-Durrmeyer variants. Several limiting cases are considered including one relating our operators to mappings investigated earlier by Mache and Zhou. A recursion formula for the moments is proved and estimates for simultaneous approximation of derivatives are given.

Bernstein-type operators on the half line

Antonio Attalienti, Michele Campiti (2002)

Czechoslovak Mathematical Journal

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We define Bernstein-type operators on the half line [ 0 , + ∞ [ by means of two sequences of strictly positive real numbers. After studying their approximation properties, we also establish a Voronovskaja-type result with respect to a suitable weighted norm.