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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 8, Issue 4


Statistical approximation of Baskakov and Baskakov-Kantorovich operators based on the q-integers

Nazim Mahmudov
Published Online: 2010-07-24 | DOI: https://doi.org/10.2478/s11533-010-0040-5


In the present paper we introduce and investigate weighted statistical approximation properties of a q-analogue of the Baskakov and Baskakov-Kantorovich operators. By using a weighted modulus of smoothness, we give some direct estimations for error in the case 0 < q < 1.

MSC: 41A36; 41A30; 41A25

Keywords: q-integers; q-Baskakov operators; q-Baskakov-Kantorovich operators; Weighted space; Weighted modulus of smoothness

  • [1] Agratini O., On statistical approximation in spaces of continuous functions, Positivity, 2009, 13(4), 735–743 http://dx.doi.org/10.1007/s11117-008-3002-4Web of ScienceCrossrefGoogle Scholar

  • [2] Altomare F., Campiti M., Korovkin-type Approximation Theory and its Applications, de Gruyter Studies in Mathematics, 17, Walter de Gruyter, Berlin-New York, 1994 Google Scholar

  • [3] Andrews G.E., Askey R., Roy R., Special Functions, Cambridge University Press, Cambridge, 1999 Google Scholar

  • [4] Aral A., Gupta V., On the Durrmeyer type modification of the q-Baskakov type operators, Nonlinear Anal., 2010, 72(3–4), 1171–1180 Google Scholar

  • [5] Baskakov V.A., An instance of a sequence of linear positive operators in the space of continuous functions, Dokl. Akad. Nauk. SSSR, 1957, 113, 249–251 (in Russian) Google Scholar

  • [6] Derriennic M.-M., Modified Bernstein polynomials and Jacobi polynomials in q-calculus, Rend. Circ. Mat. Palermo, 2005, 76, 269–290 Google Scholar

  • [7] Doğgru O., Duman O., Statistical approximation of Meyer-König and Zeller operators based on q-integers, Publ. Math. Debrecen, 2006, 68(1–2), 199–214 Google Scholar

  • [8] Doğgru O., Duman O., Orhan C., Statistical approximation by generalized Meyer-König and Zeller type operators, Studia Sci. Math. Hungar., 2003, 40(3), 359–371 Google Scholar

  • [9] Doğgru O., Gupta V., Monotonicity and the asymptotic estimate of Bleimann Butzer and Hahn operators based on q-integers, Georgian Math. J., 2005, 12(3), 415–422 Google Scholar

  • [10] Doğgru O., Gupta V., Korovkin-type approximation properties of bivariate q-Meyer-Konig and Zeller operators, Calcolo, 2006, 43(1), 51–63 http://dx.doi.org/10.1007/s10092-006-0114-8CrossrefGoogle Scholar

  • [11] Duman O., Orhan C., Statistical approximation by positive linear operators, Studia Math., 2004, 161(2), 187–197 http://dx.doi.org/10.4064/sm161-2-6CrossrefGoogle Scholar

  • [12] Gadjiev A.D., Orhan C., Some approximation theorems via statistical convergence, Rocky Mountain J. Math., 2002, 32(1), 129–138 http://dx.doi.org/10.1216/rmjm/1030539612CrossrefGoogle Scholar

  • [13] Gupta V., Some approximation properties of q-Durrmeyer operators, Appl. Math. Comput., 2008, 197(1), 172–178 http://dx.doi.org/10.1016/j.amc.2007.07.056CrossrefWeb of ScienceGoogle Scholar

  • [14] Gupta V., Radu C., Statistical approximation properties of q-Baskakov.Kantorovich operators, Cent. Eur. J. Math., 2009, 7(4), 809–818 http://dx.doi.org/10.2478/s11533-009-0055-yWeb of ScienceCrossrefGoogle Scholar

  • [15] Kac V., Cheung P., Quantum Calculus, Universitext, Springer, New York, 2002 Google Scholar

  • [16] López-Moreno A.-J., Weighted silmultaneous approximation with Baskakov type operators, Acta Math. Hungar., 2004, 104(1–2), 143–151 http://dx.doi.org/10.1023/B:AMHU.0000034368.81211.23CrossrefGoogle Scholar

  • [17] Lupaş A., A q-Analogue of the Bernstein operator, In: Seminar on Numerical and Statistical Calculus, University of Cluj-Napoca, 1987, 85–92 Google Scholar

  • [18] Mahmudov N.I., Korovkin-type theorems and applications, Cent. Eur. J. Math., 2009, 7(2), 348–356 http://dx.doi.org/10.2478/s11533-009-0006-7CrossrefWeb of ScienceGoogle Scholar

  • [19] Mahmudov N.I., On q-parametric Szász-Mirakjan operators, Mediterranean J. Math., (in press), DOI:10.1007/s00009-010-0037-0 CrossrefGoogle Scholar

  • [20] Mahmudov N.I., Sabancıgil P., q-Parametric Bleimann Butzer and Hahn operators, J. Inequal. Appl., 2008, art. ID 816367, 15 pp. Web of ScienceGoogle Scholar

  • [21] Mahmudov N.I., Sabancıgil P., On genuine q-Bernstein.Durrmeyer operators, Publ. Math. Debrecen, 2010, 76(1–2), (in press) Google Scholar

  • [22] Özarslan M.A., q-Szász Schurer operators, (in press) Google Scholar

  • [23] Phillips G.M., Bernstein polynomials based on the q-integers, Ann. Numer. Math., 1997, 4(1–4), 511–518 Google Scholar

  • [24] Radu C., On statistical approximation of a general class of positive linear operators extended in q-calculus, Appl. Math. Comput., 2009, 215(6), 2317–2325 http://dx.doi.org/10.1016/j.amc.2009.08.023CrossrefWeb of ScienceGoogle Scholar

  • [25] Trif T., Meyer-König and Zeller operators based on the q-integers, Rev. Anal. Numer. Theor. Approx., 2000, 29(2), 221–229 Google Scholar

About the article

Published Online: 2010-07-24

Published in Print: 2010-08-01

Citation Information: Open Mathematics, Volume 8, Issue 4, Pages 816–826, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-010-0040-5.

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© 2010 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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