# Bernstein type operators having 1 and x j as fixed points

Open Mathematics (2013)

- Volume: 11, Issue: 12, page 2257-2261
- ISSN: 2391-5455

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topZoltán Finta. "Bernstein type operators having 1 and x j as fixed points." Open Mathematics 11.12 (2013): 2257-2261. <http://eudml.org/doc/269514>.

@article{ZoltánFinta2013,

abstract = {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.},

author = {Zoltán Finta},

journal = {Open Mathematics},

keywords = {Bernstein type operators; Ordered normed space; Hahn-Banach type theorem; Korovkin type theorem; Bernstein-type operators; ordered normed space; Hahn-Banach-type theorem; Korovkin-type theorem},

language = {eng},

number = {12},

pages = {2257-2261},

title = {Bernstein type operators having 1 and x j as fixed points},

url = {http://eudml.org/doc/269514},

volume = {11},

year = {2013},

}

TY - JOUR

AU - Zoltán Finta

TI - Bernstein type operators having 1 and x j as fixed points

JO - Open Mathematics

PY - 2013

VL - 11

IS - 12

SP - 2257

EP - 2261

AB - 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.

LA - eng

KW - Bernstein type operators; Ordered normed space; Hahn-Banach type theorem; Korovkin type theorem; Bernstein-type operators; ordered normed space; Hahn-Banach-type theorem; Korovkin-type theorem

UR - http://eudml.org/doc/269514

ER -

## References

top- [1] Aldaz J.M., Kounchev O., Render H., Shape preserving properties of generalized Bernstein operators on extended Chebyshev spaces, Numer. Math., 2009, 114(1), 1–25 http://dx.doi.org/10.1007/s00211-009-0248-0 Zbl1184.41011
- [2] Kreĭn M.G., Rutman M.A., Linear operators leaving invariant a cone in a Banach space, Uspekhi Mat. Nauk, 1948, 3(1), 3–95 Zbl0030.12902
- [3] Lorentz G.G., Approximation of Functions, Holt, Rinehart and Winston, New York-Chicago, 1966 Zbl0153.38901
- [4] Marinescu G., Spaţii Vectoriale Normate, Editura Academiei Republicii Populare Romîne, Bucureţi, 1956

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