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Year 2016, Volume: 29 Issue: 1, 115 - 122, 21.03.2016

Ülkü Dinlemez İsmet Yüksel

Abstract

References

  • A. Aral, V. Gupta and R. P. Agarwal, Applications of q-calculus in operator theory. (Springer, New York, 2013).
  • : A. De Sole and V. G. Kac, On integral representations of q-gamma and q-beta functions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16(1), 11--29, (2005).
  • : R. A. De Vore and G. G. Lorentz, Constructive Approximation (Springer, Berlin 1993).
  • : Ü. Dinlemez, Convergence of the q-Stancu-Szasz-Beta type operators, J. Inequal. Appl., 2014:354, (2014).
  • : O. Doğru and V. Gupta, Monotonicity and the asymptotic estimate of Bleimann Butzer and Hahn operators based on q-integers. Georgian Math. J. 12(3), 415--422, (2005).
  • : O. Doğru and V. Gupta, Korovkin-type approximation properties of bivariate q -Meyer-König and Zeller operators. Calcolo 43(1), 51--63, (2006).
  • : A. D. Gadzhiev, Theorems of the type of P. P. Korovkin type theorems, Math. Zametki 20(5), 781-786, 1976; English Translation, Math. Notes, 20 (5/6), 996-998,(1976).
  • : N. K. Govil and V. Gupta, q-Beta-Szász-Stancu operators, Adv. Stud. Contemp. Math. 22(1), 117-123, (2012).
  • : V. G. Gupta, Srivastava, S. and Sahai, A. On simultaneous approximation by Szász-beta operators. Soochow J. Math. 21(1), 1--11,(1995).
  • : V. Gupta and W. Heping, The rate of convergence of q-Durrmeyer operators for 0<q<1, Math. Methods Appl. Sci. 31(16), 1946--1955, (2008).
  • : V. Gupta and A. Aral, Convergence of the q- analogue of Szász-beta operators. Appl. Math. Comput. 216(2), 374--380, (2010).
  • : V. Gupta and H. Karsli, Some approximation properties by q -Szász-Mirakyan-Baskakov-Stancu operators. Lobachevskii J. Math. 33 (2), 175--182, (2012).
  • : V. Gupta and N. I. Mahmudov, Approximation properties of the q-Szasz-Mirakjan-Beta operators, Indian J. Industrial and Appl. Math. 3(2), 41-53, (2012).
  • : F. H. Jackson, On q-definite integrals, quart. J. Pure Appl. Math., 41(15), 193-203, (1910).
  • : V. G. Kac and P. Cheung, Quantum Calculus. (Universitext. Springer-Verlag, New York, 2002).
  • : H. T. Koelink and T. H. Koornwinder, q-special functions, a tutorial. Deformation theory and quantum groups with applications to mathematical physics (Amherst, MA, 1990), 141--142, Contemp. Math., 134, Amer. Math. Soc., Providence, RI, (1992).
  • : A. A. Lupaş, q-analogue of the Bernstein operator, Seminar on numerical and statistical calculus, University of Cluj-Napoca 9, 85-92, (1987).
  • : N. I. Mahmudov, q-Szász operators which preserve x², Math. Slovaca 63(5), 1059--1072, (2013).
  • : G. M. Phillips, Bernstein polynomials based on the q-integers, Ann. Numer. Math., 4, 511-518, (1997).
  • : İ. Yüksel, Approximation by q-Phillips operators, Hacet. J. Math. Stat. 40(2), 191--201, (2011).
  • : İ. Yüksel, Direct results on the q-mixed summation integral type operators, J. Appl. Funct. Anal. 8(2), 235-245, (2013).
  • : İ. Yüksel, and Ü. Dinlemez, Voronovskaja type approximation theorem for q-Szász-beta operators, Appl. Math. Comput. 235, 555--559, (2014).
  • : İ. Yüksel, and Ü. Dinlemez, Weighted approximation by the q-Szász-Schurer-beta type operators, Gazi University Journal of Science. 28(2), 231-238, (2015).

Voronovskaja Type Approximation Theorem For 𝒒 - Szász- Beta-Stancu Type Operators

Year 2016, Volume: 29 Issue: 1, 115 - 122, 21.03.2016

Ülkü Dinlemez İsmet Yüksel

Abstract

In this paper, we study on q-analoque of  Stancu-Szász-beta type operators. We give a Voronovskaja type theorem for q-Stancu-Szász-beta type operators.

Keywords

q-Stancu type operators Szász-beta type operator Voronovskaja type theorem

References

  • A. Aral, V. Gupta and R. P. Agarwal, Applications of q-calculus in operator theory. (Springer, New York, 2013).
  • : A. De Sole and V. G. Kac, On integral representations of q-gamma and q-beta functions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16(1), 11--29, (2005).
  • : R. A. De Vore and G. G. Lorentz, Constructive Approximation (Springer, Berlin 1993).
  • : Ü. Dinlemez, Convergence of the q-Stancu-Szasz-Beta type operators, J. Inequal. Appl., 2014:354, (2014).
  • : O. Doğru and V. Gupta, Monotonicity and the asymptotic estimate of Bleimann Butzer and Hahn operators based on q-integers. Georgian Math. J. 12(3), 415--422, (2005).
  • : O. Doğru and V. Gupta, Korovkin-type approximation properties of bivariate q -Meyer-König and Zeller operators. Calcolo 43(1), 51--63, (2006).
  • : A. D. Gadzhiev, Theorems of the type of P. P. Korovkin type theorems, Math. Zametki 20(5), 781-786, 1976; English Translation, Math. Notes, 20 (5/6), 996-998,(1976).
  • : N. K. Govil and V. Gupta, q-Beta-Szász-Stancu operators, Adv. Stud. Contemp. Math. 22(1), 117-123, (2012).
  • : V. G. Gupta, Srivastava, S. and Sahai, A. On simultaneous approximation by Szász-beta operators. Soochow J. Math. 21(1), 1--11,(1995).
  • : V. Gupta and W. Heping, The rate of convergence of q-Durrmeyer operators for 0<q<1, Math. Methods Appl. Sci. 31(16), 1946--1955, (2008).
  • : V. Gupta and A. Aral, Convergence of the q- analogue of Szász-beta operators. Appl. Math. Comput. 216(2), 374--380, (2010).
  • : V. Gupta and H. Karsli, Some approximation properties by q -Szász-Mirakyan-Baskakov-Stancu operators. Lobachevskii J. Math. 33 (2), 175--182, (2012).
  • : V. Gupta and N. I. Mahmudov, Approximation properties of the q-Szasz-Mirakjan-Beta operators, Indian J. Industrial and Appl. Math. 3(2), 41-53, (2012).
  • : F. H. Jackson, On q-definite integrals, quart. J. Pure Appl. Math., 41(15), 193-203, (1910).
  • : V. G. Kac and P. Cheung, Quantum Calculus. (Universitext. Springer-Verlag, New York, 2002).
  • : H. T. Koelink and T. H. Koornwinder, q-special functions, a tutorial. Deformation theory and quantum groups with applications to mathematical physics (Amherst, MA, 1990), 141--142, Contemp. Math., 134, Amer. Math. Soc., Providence, RI, (1992).
  • : A. A. Lupaş, q-analogue of the Bernstein operator, Seminar on numerical and statistical calculus, University of Cluj-Napoca 9, 85-92, (1987).
  • : N. I. Mahmudov, q-Szász operators which preserve x², Math. Slovaca 63(5), 1059--1072, (2013).
  • : G. M. Phillips, Bernstein polynomials based on the q-integers, Ann. Numer. Math., 4, 511-518, (1997).
  • : İ. Yüksel, Approximation by q-Phillips operators, Hacet. J. Math. Stat. 40(2), 191--201, (2011).
  • : İ. Yüksel, Direct results on the q-mixed summation integral type operators, J. Appl. Funct. Anal. 8(2), 235-245, (2013).
  • : İ. Yüksel, and Ü. Dinlemez, Voronovskaja type approximation theorem for q-Szász-beta operators, Appl. Math. Comput. 235, 555--559, (2014).
  • : İ. Yüksel, and Ü. Dinlemez, Weighted approximation by the q-Szász-Schurer-beta type operators, Gazi University Journal of Science. 28(2), 231-238, (2015).
There are 23 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Ülkü Dinlemez

İsmet Yüksel

Publication Date March 21, 2016
Published in Issue Year 2016 Volume: 29 Issue: 1

Cite

APA Dinlemez, Ü., & Yüksel, İ. (2016). Voronovskaja Type Approximation Theorem For 𝒒 - Szász- Beta-Stancu Type Operators. Gazi University Journal of Science, 29(1), 115-122.
AMA Dinlemez Ü, Yüksel İ. Voronovskaja Type Approximation Theorem For 𝒒 - Szász- Beta-Stancu Type Operators. Gazi University Journal of Science. March 2016;29(1):115-122.
Chicago Dinlemez, Ülkü, and İsmet Yüksel. “Voronovskaja Type Approximation Theorem For 𝒒 - Szász- Beta-Stancu Type Operators”. Gazi University Journal of Science 29, no. 1 (March 2016): 115-22.
EndNote Dinlemez Ü, Yüksel İ (March 1, 2016) Voronovskaja Type Approximation Theorem For 𝒒 - Szász- Beta-Stancu Type Operators. Gazi University Journal of Science 29 1 115–122.
IEEE Ü. Dinlemez and İ. Yüksel, “Voronovskaja Type Approximation Theorem For 𝒒 - Szász- Beta-Stancu Type Operators”, Gazi University Journal of Science, vol. 29, no. 1, pp. 115–122, 2016.
ISNAD Dinlemez, Ülkü - Yüksel, İsmet. “Voronovskaja Type Approximation Theorem For 𝒒 - Szász- Beta-Stancu Type Operators”. Gazi University Journal of Science 29/1 (March 2016), 115-122.
JAMA Dinlemez Ü, Yüksel İ. Voronovskaja Type Approximation Theorem For 𝒒 - Szász- Beta-Stancu Type Operators. Gazi University Journal of Science. 2016;29:115–122.
MLA Dinlemez, Ülkü and İsmet Yüksel. “Voronovskaja Type Approximation Theorem For 𝒒 - Szász- Beta-Stancu Type Operators”. Gazi University Journal of Science, vol. 29, no. 1, 2016, pp. 115-22.
Vancouver Dinlemez Ü, Yüksel İ. Voronovskaja Type Approximation Theorem For 𝒒 - Szász- Beta-Stancu Type Operators. Gazi University Journal of Science. 2016;29(1):115-22.