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Voronovskaja Type Approximation Theorem for q-Szasz–Schurer Operators

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Computational Analysis

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 155))

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Abstract

In 2011, Özarslan (Miscolc Math Notes, 12:225–235, 2011) introduced the q-Szasz–Schurer operators and investigated their approximation properties. In the present paper, we state the Voronovskaja-type asymptotic formula for q-analogue of Szasz–Schurer operators.

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References

  1. A. Acar, V. Gupta, A. Aral, Rate of convergence for generalized Szsaz operators. Bull. Math. Sci. 1, 99–113 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  2. P.N. Agrawal, V. Gupta, S.A. Kumar, On a q-analogue of Bernstein-Schurer-Stancu operators. Appl. Math. Comput. 219, 7754–7764 (2013)

    MathSciNet  MATH  Google Scholar 

  3. F. Altomare, M. Campiti, Korovkin-Type Approximation Theory and Its Applications. De Gruyter Studies in Mathematics, vol. 17 (Walter de Gruyter, Berlin, 1994)

    Google Scholar 

  4. A. Aral, A generalization of Szasz-Mirakyan operators based on q-integers. Math. Comput. Model. 47 (9–10), 1052–1062 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. A. Aral, V. Gupta, The q-derivative and applications to q-Szasz Mirakyan operators. Calcolo 43 (3), 151–170 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Becker, Global approximation theorems for Szasz-Mirakyan and Baskakov operators in polynomial weight spaces. Indiana Univ. Math. J. 27 (1), 151–170 (2006)

    Google Scholar 

  7. I. Büyükyazıcı, H. Sharma, Approximation properties of two-dimensional q-Bernstein-Chlodowsky-Durrmeyer operators. Numer. Funct. Anal. Optim. 33 (2), 1351–1371 (2012)

    MathSciNet  MATH  Google Scholar 

  8. Q.-B. Cai, X.-M. Zeng, Z. Cui, Approximation properties of the modification of Kantorovich type q-Szasz operators. J. Comput. Anal. Appl. 15 (1), 176–187 (2013)

    MathSciNet  MATH  Google Scholar 

  9. N. Deo, Simultaneous approximation by Lupaş modified operators with weighted function of Szasz operators. J. Inequal. Pure Appl. Math. 5 (4), 5 pp. (2014)

    Google Scholar 

  10. R.A. DeVore, G.G. Lorentz, Constructive Approximation (Springer, Berlin, 1993)

    Book  MATH  Google Scholar 

  11. O. Duman, M.A. Özarslan, Szasz-Mirakjan type operators providing a better error estimation. Appl. Math. Lett. 20, 1184–1188 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. S.G. Gal, N.I. Mahmudov, K. Kara, Approximation by complex q-Szasz Kantorovich operators in compact disks, q > 1. Complex Anal. Oper. Theory 7, 1853–1867 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  13. V. Gupta, A note on modified Szasz operators. Bull. Inst. Math. Acad. Sin. 21 (3), 275–278 (1993)

    MathSciNet  MATH  Google Scholar 

  14. V. Gupta, A note on q-Baskakov-Szasz operators. Lobachevskii J. Math. 31 (4), 359–366 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. V. Gupta, A Stancu variant of Beta Szasz operators. Georgian Math. J. 21 (1), 75–82 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  16. V. Kac, P. Cheung, Quantum Calculus (Springer, Berlin, 2002)

    Book  MATH  Google Scholar 

  17. A.A. Lupaş, q-Analogue of the Bernstein operators. Semin. Numer. Stat. Calculus, Univ. Cluj-Napoca 9, 85–92 (1987)

    Google Scholar 

  18. N.I. Mahmudov, Approximation by q-Szasz operators (2010). arXiv:1005.3934 [math.FA]

    Google Scholar 

  19. N.I. Mahmudov, On q-parametric Szasz-Mirakyan operators. Mediterr. J. Math. 7 (3), 297–311 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  20. N.I. Mahmudov, q-Szasz operators which preserve x 2. Math. Slovaca 63 (5), 1059–1072 (2013)

    Google Scholar 

  21. N.I. Mahmudov, V. Gupta, On certain q-analogue of Szasz Kantorovich operators. J. Appl. Math. Comput. 37 (1–2), 407–419 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  22. C.V. Muraru, Note on q-Bernstein-Schurer operators. Babeş-Bolyaj Math. 56, 489–495 (2011)

    MathSciNet  Google Scholar 

  23. M. Örkcü, Approximation properties of bivariate extension of q-Szasz-Mirakjan-Kantorovich operators. J. Inequal. Appl. 324, 10 pp. (2013)

    Google Scholar 

  24. M. Örkcü, O. Doğru, q-Szasz-Mirakyan-Kantorovich type operators preserving some test functions. Appl. Math. Lett. 24 (9), 1588–1593 (2011)

    Google Scholar 

  25. M. Örkcü, O. Doğru, Statistical approximation of a kind of Kantorovich type q-Szasz-Mirakjan operators. Nonlinear Anal. Theory Methods Appl. 75 (5), 2874–2882 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  26. M.A. Özarslan, q-Szasz Schurer operators. Miscolc Math. Notes 12, 225–235 (2011)

    Google Scholar 

  27. M.A. Özarslan, T. Vedi, q-Bernstein-Schurer-Kantorovich Operators. J. Inequal. Appl. 444, 15 pp. (2013)

    Google Scholar 

  28. G.M. Phillips, On generalized Bernstein polynomials, in Numerical Analysis, vol. 98 (World Scientific, River Edge, 1996), pp. 263–269

    Google Scholar 

  29. T. Vedi, M.A. Özarslan, Some properties of q-Bernstein-Schurer operators. J. Appl. Funct. Anal. 8 (1), 45–53 (2013)

    MathSciNet  MATH  Google Scholar 

  30. İ. Yüksel, Ü. Dinlemez, Voronovskaja type approximation theorem for q-Szasz-beta operators. Appl. Math. Comput. 235, 555–559 (2014)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Eastern Mediterranean University, Famagusta, North Cyprus, Cyprus

    Tuba Vedi & Mehmet Ali Özarslan

Authors
  1. Tuba Vedi
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  2. Mehmet Ali Özarslan
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Corresponding author

Correspondence to Tuba Vedi .

Editor information

Editors and Affiliations

  1. Dept of Mathematical Sciences, University of Memphis, Memphis, Tennessee, USA

    George A. Anastassiou

  2. Department of Mathematics, TOBB Univ. of Economics and Technology, Ankara, Ankara, Turkey

    Oktay Duman

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Vedi, T., Özarslan, M.A. (2016). Voronovskaja Type Approximation Theorem for q-Szasz–Schurer Operators. In: Anastassiou, G., Duman, O. (eds) Computational Analysis. Springer Proceedings in Mathematics & Statistics, vol 155. Springer, Cham. https://doi.org/10.1007/978-3-319-28443-9_25

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