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Weighted Approximation by the 𝒒 −Szász−Schurer−Beta Type Operators

Yıl 2015, Cilt: 28 Sayı: 2, 231 - 238, 22.06.2015

Öz

In this study, we investigate approximation properties of a Schurer type generalization of q-Szász-beta type operators. We estimate the rate of weighted approximation of these operators for functions of polynomial growth on the interval [0,∞).

Kaynakça

  • Lupaş, A., A −analogue of the Bernstein operator, Seminar on numerical and statistical calculus, University of Cluj-Napoca 9 (1987) 85-92.
  • Phillips, G. M.,Bernstein polynomials based on the q-integers, Ann. Numer. Math. 4 (1997) 511-518.
  • Doğru, O. and Gupta, V., Monotonicity and the asymptotic estimate of Bleimann Butzer and Hahn operators based on q -integers, Georgian Math. J. 12 (2005) (3) 415-422.
  • Doğru, O. and Gupta, V., Korovkin-type approximation properties of bivariate −Meyer- König and Zeller operators, Calcolo 43 (1) (2006) 51-63.
  • Gupta, V. and Aral, A., Convergence of the −analogue of Szász-beta operators, Appl. Math. Comput., 216 (2) (2010) 374-380.
  • Gupta, V. and Karslı, H., Some approximation properties by Szász -Mirakyan-Baskakov- Stancu operators, Lobachevskii J. Math. 33(2) (2012) 175-182.
  • Yüksel, İ., Approximation by −Phillips operators, Hacet. J. Math. Stat. 40 (2011) no. 2, 191-201.
  • Yüksel,·İ., Direct results on the −mixed summation integral type operators, J. Appl. Funct. Anal. (2) (2013) 235-245.
  • Dinlemez, Ü., Yüksel ·İ. and Altın, B., A note on the approximation by the −hybrid summation integral type operators, Taiwanese J. Math. 18(3) (2014) 781
  • Gupta, V. and Mahmudov, N. I., Approximation properties of the −Szasz-Mirakjan-Beta operators, Indian J. Industrial and Appl. Math. 3(2) (20012) 41-53.
  • Yüksel, İ. and Dinlemez, Ü., Voronovskaja type approximation theorem for −Szász-beta operators. Appl. Math. Comput. 235 (2014) 555-559.
  • Govil, N. K. and Gupta, V., −Beta-Szász-Stancu operators. Adv. Stud. Contemp. Math. 22(1) (2012) 123
  • Mahmudov, N. I., −Szász operators which preserve x2 . Slovaca 63(5) (2013) 1059-1072
  • Dinlemez, Ü., Convergence of the −Stancu- Szasz-beta type operators, J. Inequal. Appl. 2014, :354, 8 pp.
  • Jackson, F. H., On −definite integrals, quart. J. Pure Appl. Math., 41(15) (1910) 193-203.
  • Koelink, H. T. and Koornwinder, T. H., −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.
  • Kac, V. G. and Cheung, P., Quantum calculus, Universitext. Springer-Verlag, New York, 2002.
  • De Sole, A. and Kac, V. G., On integral representations of −gamma and −beta functions, Atti. Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 16(1) (2005) 11-29.
  • Aral, A., Gupta, V. and Agarwal, R. P., Applications of q-calculus in operator theory, Springer, New York, 2013.
  • Gupta, V., Srivastava, G. S. and Sahai, A., On simultaneous approximation by Szász-beta operators, Soochow J. Math. 21(1) (1995) 1-11.
  • Gupta V. and Agarwal, R. P., Convergence estimates in approximation theory. Springer, Cham, ISBN: 978-3-319-02764-7 2014.
  • Deo, N., Direct result on the Durrmeyer variant of Beta operators. Southeast Asian Bull. Math. 32(2) (2008) 283-290.
  • Deo, N., Direct result on exponential-type operators. Appl. Math. Comput. 204(1) (2008) 109-115
  • De Vore R. A. and Lorentz, G. G., Constructive Approximation, Springer, Berlin 1993.
  • Gadzhiev, A. D., Theorems of the type of P. P. Korovkin type theorems, Math. Zametki 20(5) (1976) 786; English Translation, Math. Notes, 20(5/6) (1976) 996-998.
  • İspir, N., On modified Baskakov operators on weighted spaces, Turkish J. Math. 25(3) (2001) 355
Yıl 2015, Cilt: 28 Sayı: 2, 231 - 238, 22.06.2015

Öz

Kaynakça

  • Lupaş, A., A −analogue of the Bernstein operator, Seminar on numerical and statistical calculus, University of Cluj-Napoca 9 (1987) 85-92.
  • Phillips, G. M.,Bernstein polynomials based on the q-integers, Ann. Numer. Math. 4 (1997) 511-518.
  • Doğru, O. and Gupta, V., Monotonicity and the asymptotic estimate of Bleimann Butzer and Hahn operators based on q -integers, Georgian Math. J. 12 (2005) (3) 415-422.
  • Doğru, O. and Gupta, V., Korovkin-type approximation properties of bivariate −Meyer- König and Zeller operators, Calcolo 43 (1) (2006) 51-63.
  • Gupta, V. and Aral, A., Convergence of the −analogue of Szász-beta operators, Appl. Math. Comput., 216 (2) (2010) 374-380.
  • Gupta, V. and Karslı, H., Some approximation properties by Szász -Mirakyan-Baskakov- Stancu operators, Lobachevskii J. Math. 33(2) (2012) 175-182.
  • Yüksel, İ., Approximation by −Phillips operators, Hacet. J. Math. Stat. 40 (2011) no. 2, 191-201.
  • Yüksel,·İ., Direct results on the −mixed summation integral type operators, J. Appl. Funct. Anal. (2) (2013) 235-245.
  • Dinlemez, Ü., Yüksel ·İ. and Altın, B., A note on the approximation by the −hybrid summation integral type operators, Taiwanese J. Math. 18(3) (2014) 781
  • Gupta, V. and Mahmudov, N. I., Approximation properties of the −Szasz-Mirakjan-Beta operators, Indian J. Industrial and Appl. Math. 3(2) (20012) 41-53.
  • Yüksel, İ. and Dinlemez, Ü., Voronovskaja type approximation theorem for −Szász-beta operators. Appl. Math. Comput. 235 (2014) 555-559.
  • Govil, N. K. and Gupta, V., −Beta-Szász-Stancu operators. Adv. Stud. Contemp. Math. 22(1) (2012) 123
  • Mahmudov, N. I., −Szász operators which preserve x2 . Slovaca 63(5) (2013) 1059-1072
  • Dinlemez, Ü., Convergence of the −Stancu- Szasz-beta type operators, J. Inequal. Appl. 2014, :354, 8 pp.
  • Jackson, F. H., On −definite integrals, quart. J. Pure Appl. Math., 41(15) (1910) 193-203.
  • Koelink, H. T. and Koornwinder, T. H., −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.
  • Kac, V. G. and Cheung, P., Quantum calculus, Universitext. Springer-Verlag, New York, 2002.
  • De Sole, A. and Kac, V. G., On integral representations of −gamma and −beta functions, Atti. Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 16(1) (2005) 11-29.
  • Aral, A., Gupta, V. and Agarwal, R. P., Applications of q-calculus in operator theory, Springer, New York, 2013.
  • Gupta, V., Srivastava, G. S. and Sahai, A., On simultaneous approximation by Szász-beta operators, Soochow J. Math. 21(1) (1995) 1-11.
  • Gupta V. and Agarwal, R. P., Convergence estimates in approximation theory. Springer, Cham, ISBN: 978-3-319-02764-7 2014.
  • Deo, N., Direct result on the Durrmeyer variant of Beta operators. Southeast Asian Bull. Math. 32(2) (2008) 283-290.
  • Deo, N., Direct result on exponential-type operators. Appl. Math. Comput. 204(1) (2008) 109-115
  • De Vore R. A. and Lorentz, G. G., Constructive Approximation, Springer, Berlin 1993.
  • Gadzhiev, A. D., Theorems of the type of P. P. Korovkin type theorems, Math. Zametki 20(5) (1976) 786; English Translation, Math. Notes, 20(5/6) (1976) 996-998.
  • İspir, N., On modified Baskakov operators on weighted spaces, Turkish J. Math. 25(3) (2001) 355
Toplam 27 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Mathematics
Yazarlar

İsmet Yüksel

Ülkü Dinlemez

Yayımlanma Tarihi 22 Haziran 2015
Yayımlandığı Sayı Yıl 2015 Cilt: 28 Sayı: 2

Kaynak Göster

APA Yüksel, İ., & Dinlemez, Ü. (2015). Weighted Approximation by the 𝒒 −Szász−Schurer−Beta Type Operators. Gazi University Journal of Science, 28(2), 231-238.
AMA Yüksel İ, Dinlemez Ü. Weighted Approximation by the 𝒒 −Szász−Schurer−Beta Type Operators. Gazi University Journal of Science. Haziran 2015;28(2):231-238.
Chicago Yüksel, İsmet, ve Ülkü Dinlemez. “Weighted Approximation by the 𝒒 −Szász−Schurer−Beta Type Operators”. Gazi University Journal of Science 28, sy. 2 (Haziran 2015): 231-38.
EndNote Yüksel İ, Dinlemez Ü (01 Haziran 2015) Weighted Approximation by the 𝒒 −Szász−Schurer−Beta Type Operators. Gazi University Journal of Science 28 2 231–238.
IEEE İ. Yüksel ve Ü. Dinlemez, “Weighted Approximation by the 𝒒 −Szász−Schurer−Beta Type Operators”, Gazi University Journal of Science, c. 28, sy. 2, ss. 231–238, 2015.
ISNAD Yüksel, İsmet - Dinlemez, Ülkü. “Weighted Approximation by the 𝒒 −Szász−Schurer−Beta Type Operators”. Gazi University Journal of Science 28/2 (Haziran 2015), 231-238.
JAMA Yüksel İ, Dinlemez Ü. Weighted Approximation by the 𝒒 −Szász−Schurer−Beta Type Operators. Gazi University Journal of Science. 2015;28:231–238.
MLA Yüksel, İsmet ve Ülkü Dinlemez. “Weighted Approximation by the 𝒒 −Szász−Schurer−Beta Type Operators”. Gazi University Journal of Science, c. 28, sy. 2, 2015, ss. 231-8.
Vancouver Yüksel İ, Dinlemez Ü. Weighted Approximation by the 𝒒 −Szász−Schurer−Beta Type Operators. Gazi University Journal of Science. 2015;28(2):231-8.