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2009 | 7 | 2 | 348-356
Tytuł artykułu

Korovkin-type theorems and applications

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let {T n} be a sequence of linear operators on C[0,1], satisfying that {T n (e i)} converge in C[0,1] (not necessarily to e i) for i = 0,1,2, where e i = t i. We prove Korovkin-type theorem and give quantitative results on C 2[0,1] and C[0,1] for such sequences. Furthermore, we define King’s type q-Bernstein operator and give quantitative results for the approximation properties of such operators.
Wydawca
Czasopismo
Rocznik
Tom
7
Numer
2
Strony
348-356
Opis fizyczny
Daty
wydano
2009-06-01
online
2009-05-24
Twórcy
Bibliografia
  • [1] DeVore R.A., Lorentz G.G., Constructive approximation, Springer, Berlin, 1993
  • [2] Doğru O., Gupta V., Korovkin-type approximation properties of bivariate q-Meyer-König and Zeller operators, Calcolo, 2006, 43, 51–63 http://dx.doi.org/10.1007/s10092-006-0114-8[Crossref]
  • [3] Gonska H., Pițul P., Remarks on an article of J.P. King, Comment. Math. Univ. Carolin., 2005, 46, 645–652
  • [4] Heping W., Korovkin-type theorem and application, J. Approx. Theory, 2005, 132, 258–264 http://dx.doi.org/10.1016/j.jat.2004.12.010[Crossref]
  • [5] Heping W., XueZhi W., Saturation of convergence for q-Bernstein polynomials in the case q ≥ 1, J. Math. Anal. Appl., 2008, 337, 744–750 http://dx.doi.org/10.1016/j.jmaa.2007.04.014[Crossref][WoS]
  • [6] Il’inskii A., Ostrovska S., Convergence of generalized Bernstein polynomials, J. Approx. Theory, 2002, 116, 100–112 http://dx.doi.org/10.1006/jath.2001.3657[Crossref]
  • [7] King J.P., Positive linear operators which preserve x 2, Acta. Math. Hungar., 2003, 99, 203–208 http://dx.doi.org/10.1023/A:1024571126455[Crossref]
  • [8] Lupaș A., A q-analogue of the Bernstein operator, University of Cluj-Napoca, Seminar on numerical and statistical calculus, 1987, 85–92
  • [9] Muñoz-Delgado F.J., Cárdenas-Morales D., Almost convexity and quantitative Korovkin type results, Appl. Math. Lett., 1998, 11, 105–108 http://dx.doi.org/10.1016/S0893-9659(98)00065-2[Crossref]
  • [10] Ostrovska S., q-Bernstein polynomials and their iterates, J. Approx. Theory, 2003, 123, 232–255 http://dx.doi.org/10.1016/S0021-9045(03)00104-7[Crossref]
  • [11] Ostrovska S., The first decade of the q-Bernstein polynomials: results and perspectives, Journal of Mathematical Analysis and Approximation Theory, 2007, 2, 35–51
  • [12] Phillips G.M., Bernstein polynomials based on the q-integers, Ann. Numer. Math., 1997, 4, 511–518
  • [13] Phillips G.M., Interpolation and approximation by polynomials, Springer-Verlag, New York, 2003
  • [14] Trif T., Meyer-König and Zeller operators based on the q-integers, Rev. Anal. Numer. Theory Approx., 2000, 29, 221–229
  • [15] Videnskii V.S., On some classes of q-parametric positive linear operators, Oper. Theory Adv. Appl., 2005, 158, 213–222 http://dx.doi.org/10.1007/3-7643-7340-7_15[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0006-7
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