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Bernstein type operators having 1 and x j as fixed points

Zoltán Finta (2013)

Open Mathematics

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.

Bernstein-type operators on the half line

Antonio Attalienti, Michele Campiti (2002)

Czechoslovak Mathematical Journal

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.

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