Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Open Mathematics

formerly Central European Journal of Mathematics

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

1 Issue per year


IMPACT FACTOR 2016 (Open Mathematics): 0.682
IMPACT FACTOR 2016 (Central European Journal of Mathematics): 0.489

CiteScore 2016: 0.62

SCImago Journal Rank (SJR) 2016: 0.454
Source Normalized Impact per Paper (SNIP) 2016: 0.850

Mathematical Citation Quotient (MCQ) 2016: 0.23

Open Access
Online
ISSN
2391-5455
See all formats and pricing
More options …
Volume 8, Issue 4 (Aug 2010)

Issues

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

Abstract

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, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-010-0040-5.

Export Citation

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

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
P. N. Agrawal, Meenu Goyal, and Arun Kajla
Bollettino dell'Unione Matematica Italiana, 2015, Volume 8, Number 3, Page 169
[2]
Mohammad Mursaleen, Md Nasiruzzaman, and Ashirbayev Nurgali
Journal of Inequalities and Applications, 2015, Volume 2015, Number 1
[3]
P. N. Agrawal, Zoltán Finta, and A. Sathish Kumar
Results in Mathematics, 2015, Volume 67, Number 3-4, Page 365
[4]
[5]
M. Mursaleen and Asif Khan
Journal of Function Spaces and Applications, 2013, Volume 2013, Page 1
[6]
Mediha Örkcü
Journal of Inequalities and Applications, 2013, Volume 2013, Number 1, Page 324
[7]
N. I. Mahmudov
Abstract and Applied Analysis, 2012, Volume 2012, Page 1
[8]
Mediha Örkcü and Ogün Doğru
Nonlinear Analysis: Theory, Methods & Applications, 2012, Volume 75, Number 5, Page 2874

Comments (0)

Please log in or register to comment.
Log in