Research Article
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Year 2016, Volume 29, Issue 1, 115 - 122, 21.03.2016

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

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.

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).

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

Bibtex @research article { gujs264279, journal = {Gazi University Journal of Science}, eissn = {2147-1762}, address = {}, publisher = {Gazi University}, year = {2016}, volume = {29}, number = {1}, pages = {115 - 122}, title = {Voronovskaja Type Approximation Theorem For 𝒒 - Szász- Beta-Stancu Type Operators}, key = {cite}, author = {Dinlemez, Ülkü and Yüksel, İsmet} }
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 . Retrieved from https://dergipark.org.tr/en/pub/gujs/issue/25028/264279
MLA Dinlemez, Ü. , Yüksel, İ. "Voronovskaja Type Approximation Theorem For 𝒒 - Szász- Beta-Stancu Type Operators" . Gazi University Journal of Science 29 (2016 ): 115-122 <https://dergipark.org.tr/en/pub/gujs/issue/25028/264279>
Chicago Dinlemez, Ü. , Yüksel, İ. "Voronovskaja Type Approximation Theorem For 𝒒 - Szász- Beta-Stancu Type Operators". Gazi University Journal of Science 29 (2016 ): 115-122
RIS TY - JOUR T1 - Voronovskaja Type Approximation Theorem For 𝒒 - Szász- Beta-Stancu Type Operators AU - ÜlküDinlemez, İsmetYüksel Y1 - 2016 PY - 2016 N1 - DO - T2 - Gazi University Journal of Science JF - Journal JO - JOR SP - 115 EP - 122 VL - 29 IS - 1 SN - -2147-1762 M3 - UR - Y2 - 2023 ER -
EndNote %0 Gazi University Journal of Science Voronovskaja Type Approximation Theorem For 𝒒 - Szász- Beta-Stancu Type Operators %A Ülkü Dinlemez , İsmet Yüksel %T Voronovskaja Type Approximation Theorem For 𝒒 - Szász- Beta-Stancu Type Operators %D 2016 %J Gazi University Journal of Science %P -2147-1762 %V 29 %N 1 %R %U
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 .
AMA Dinlemez Ü. , Yüksel İ. Voronovskaja Type Approximation Theorem For 𝒒 - Szász- Beta-Stancu Type Operators. Gazi University Journal of Science. 2016; 29(1): 115-122.
Vancouver Dinlemez Ü. , Yüksel İ. Voronovskaja Type Approximation Theorem For 𝒒 - Szász- Beta-Stancu Type Operators. Gazi University Journal of Science. 2016; 29(1): 115-122.
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, Mar. 2016