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2009 | 7 | 4 | 809-818
Tytuł artykułu

Statistical approximation properties of q-Baskakov-Kantorovich operators

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the present paper we introduce a q-analogue of the Baskakov-Kantorovich operators and investigate their weighted statistical approximation properties. By using a weighted modulus of smoothness, we give some direct estimations for error in case 0 < q < 1.
Wydawca
Czasopismo
Rocznik
Tom
7
Numer
4
Strony
809-818
Opis fizyczny
Daty
wydano
2009-12-01
online
2009-10-31
Twórcy
autor
  • School of Applied Sciences, Netaji Subhas Institute of Technology, Sector 3 Dwarka, New Delhi, India, vijaygupta2001@hotmail.com
Bibliografia
  • [1] Abel U., Gupta V., An estimate of the rate of convergence of a Bezier variant of the Baskakov-Kantorovich operators for bounded variation functions, Demonstratio Math., 2003, 36, 123–136
  • [2] Agratini O., On statistical approximation in spaces of continuous functions, Positivity, 2009, 13, 735–743 http://dx.doi.org/10.1007/s11117-008-3002-4[WoS][Crossref]
  • [3] Andrews G.E., Askey R., Roy R., Special functions, Cambridge Univ. Press., 1999
  • [4] Aral A., Gupta V., On the Durrmeyer type modification of the q-Baskakov type operators, Nonlinear Anal., (in press), DOI: 10.1016/j.na.2009.07.052 [Crossref]
  • [5] Baskakov V.A., An example of a sequence of linear positive operators in the space of continuous functions, Dokl. Akad. Nauk. SSSR, 1957, 113, 249–251 (in Russian)
  • [6] Derriennic M.-M., Modified Bernstein polynomials and Jacobi polynomials in q-calculus, Rend. Circ. Mat. Palermo Serie II, 2005, 76, 269–290
  • [7] Doǧru O., Duman O., Statistical approximation of Meyer-König and Zeller operators based on q-integers, Publ. Math. Debrecen, 2006, 68, 199–214
  • [8] Dogru O., Duman O., Orhan C., Statistical approximation by generalized Meyer-König and Zeller type operators, Studia Sci. Math. Hungar., 2003, 40, 359–371
  • [9] Dogru O., Gupta V., Monotonicity and the asymptotic estimate of Bleimann Butzer and Hahn operators based on q-integers, Georgian Math. J., 2005, 12, 415–422
  • [10] Doǧru 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]
  • [11] Duman O., Orhan C., Statistical approximation by positive linear operators, Studia Math., 2006, 161, 187–197 http://dx.doi.org/10.4064/sm161-2-6[Crossref]
  • [12] Ernst T., The history of q-calculus and a new method, U.U.D.M. Report 2000, 16, Uppsala, Departament of Mathematics, Uppsala University, 2000
  • [13] Gupta V., Some approximation properties of q-Durrmeyer operators, Appl. Math. Comput., 2008, 197, 172–178 http://dx.doi.org/10.1016/j.amc.2007.07.056[Crossref][WoS]
  • [14] Kac V., Cheung P., Quantum calculus, Universitext, Springer-Verlag, New York, 2002
  • [15] López-Moreno A.-J., Weighted silmultaneous approximation with Baskakov type operators, Acta Math. Hungar., 2004, 104, 143–151 http://dx.doi.org/10.1023/B:AMHU.0000034368.81211.23[Crossref]
  • [16] Lorentz G.G., Bernstein polynomials, Math. Expo. Vol. 8, Univ. of Toronto Press, Toronto, 1953
  • [17] Phillips G.M., Bernstein polynomials based on the q-integers, Ann. Numer. Math., 1997, 4, 511–518
  • [18] Radu C., Statistical approximation properties of Kantorovich operators based on q-integers, Creat. Math. Inform., 2008, 17, 75–84
  • [19] Trif T., Meyer-König and Zeller operators based on the q-integers, Rev. Anal. Numér. Théor. Approx., 2000, 29, 221–229
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-009-0055-y
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