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.
@article{bwmeta1.element.doi-10_2478_s11533-013-0310-0,
author = {Zolt\'an Finta},
title = {Bernstein type operators having 1 and x j as fixed points},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {2257-2261},
zbl = {1284.41015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0310-0}
}
Zoltán Finta. Bernstein type operators having 1 and x j as fixed points. Open Mathematics, Tome 11 (2013) pp. 2257-2261. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0310-0/
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