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Bernstein type operators having 1 and x j as fixed points

100%

Finta Z.

Open Mathematics

2013

tom 11

nr 12

2257-2261

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.

Statistical approximation for periodic functions

88%

Duman O.

Demonstratio Mathematica

2003

tom Vol. 36, nr 4

873--878

In this paper we study a Korovkin type approximation theorem for positive linear operators on the space of all 2π-periodic and continuous functions on the whole real axis via A-statistical convergence.

Some properties of modified Szász-Mirakyan operators in polynomial spaces via the power summability method

51%

Braha N. L.

2020

tom Vol. 26, nr 1

79--90

In this paperwe will prove the Korovkin type theorem for modified Szász-Mirakyan operators via Astatistical convergence and the power summability method. Also we give the rate of the convergence related to the above summability methods, and in the last section, we give a kind of Voronovskaya type theorem for A-statistical convergence and Grüss-Voronovskaya type theorem.