Bernstein type operators having 1 and x j as fixed points

• Autorzy: Zoltán Finta
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 41A10: Approximation by polynomials
• 41A36: Approximation by positive operators

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 12
• Strony: 2257-2261

Daty

wydano

2013-12-01

online

2013-10-08

Twórcy

autor

Zoltán Finta

• Babeş-Bolyai University

Bibliografia

• [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
• [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
• [3] Lorentz G.G., Approximation of Functions, Holt, Rinehart and Winston, New York-Chicago, 1966
• [4] Marinescu G., Spaţii Vectoriale Normate, Editura Academiei Republicii Populare Romîne, Bucureţi, 1956

Identyfikatory

DOI

10.2478/s11533-013-0310-0