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On a New Type of q-Baskakov Operators

Yıl 2018, Cilt: 22 Sayı: 1, 121 - 125, 29.03.2018

Öz

In this work, we have introduced a new type of $q$-analogous of Baskakov Operators.  Their respective formulae for central moments are thereby obtained. The approximation properties and the approximation rapid of the sequences of the operators which are defined have been established in terms of the  modulus of smoothness.

Kaynakça

  • [1] Jackson, F. H. 1908. On q-functions and a certain difference operator. Transactions Royal Society Edinburgh, 46(1908), 253-281.
  • [2] Aral, A., Gupta and V., Agarwal, R. P. 2013. Applications of q-Calculus in Operator Theory. Springer-Verlag New York, 262s.
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  • [4] Ernst, T. 2000. The History of q-Calculus and a New Method. U.U.D.M. Report Uppsala, Department of Mathematics, Uppsala University, 230s.
  • [5] Lupas, A. 1987. A q-analogue of the Bernstein operator. University of Cluj-Napoca Seminar on numerical and statistical calculus, 9(1987), 85-92.
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  • [8] Heping, W., Meng, F. 2005. The rate of convergence of q-Bernstein polynomials for 0 < q < 1. Journal of Approximation Theory, 136(2005), 151-158.
  • [9] II’inski, A., Ostrovska, S. 2002. Convergence of generalized Bernstein polynomials. Journal of Approximation Theory, 116(2002), 100-112.
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  • [11] Bustamante, J. 2017. Bernstein operators and their properties. Birkhäuser Basel, 420s.
  • [12] Kajla, A., Ispir, N., Agrawal, P.N., Goyal, M. 2016. q-Bernstein-Schurer-Durrmeyer type operators for functions of one and two variables. Applied Mathematics and Computation, 275(2016), 372-385.
  • [13] Agrawal, P.N., Goyal, M., Kajla, A. 2015. q-Bernstein-Schurer-Durrmeyer type operators for functions of one and two variables. Bollettino dell’Unione Matematica Italiana, 8(2015) , 169–180.
  • [14] Baskakov, V. A. 1957. An example of sequence of linear positive operators in the space of continuous functions. Doklady Akademii Nauk SSSR, 113(1957), 259-251.
  • [15] Aral, A., Gupta, V. 2009. On q-Baskakov type operators. Demonstratio Mathematica, 42(1)(2009), 109-122.
  • [16] Aral, A., Gupta, V. 2011. Generalized q-Baskakov operators. Mathematica Slovaca, 61(4)(2011), 619-634.
  • [17] Radu, C. 2009. On statistical approximation of a general class of positive linear operators extended in q-calculus. Applied Mathematics and Computation, 215(6)(2009), 2317-2325.
  • [18] Korovkin, P. P. 1960. Linear Operators and Approximation Theory. Hindustan Pub. Corp., 222s.
  • [19] Simsek, E., Tunc, T. 2017. On the Construction of q- Analogues for some Positive Linear Operators. Filomat, 31:13 (2017), 4287-4295.
  • [20] Simsek E., Tunc, T. 2018. On Approximation Properties of some Class Positive Linear Operators in q-Analysis. Journal of Mathematical Inequalities, Accepted (2018).
  • [21] Rajkovic, P. M., Stankovic, M. S., Marinkovic, S. D. 2002. Mean value theorems in q-calculus. Applied Mathematics and Computation, 54(2002), 171-178.
  • [22] Carlitz, L. 1948. q-Bernoulli numbers and polynomials. Duke Mathematical Journal, 63(1948), 987-1000.
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Bölüm Makaleler
Yazarlar

Ersin Şimşek

Yayımlanma Tarihi 29 Mart 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 22 Sayı: 1

Kaynak Göster

APA Şimşek, E. (2018). On a New Type of q-Baskakov Operators. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22(1), 121-125. https://doi.org/10.19113/sdufbed.29379
AMA Şimşek E. On a New Type of q-Baskakov Operators. SDÜ Fen Bil Enst Der. Nisan 2018;22(1):121-125. doi:10.19113/sdufbed.29379
Chicago Şimşek, Ersin. “On a New Type of Q-Baskakov Operators”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22, sy. 1 (Nisan 2018): 121-25. https://doi.org/10.19113/sdufbed.29379.
EndNote Şimşek E (01 Nisan 2018) On a New Type of q-Baskakov Operators. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 1 121–125.
IEEE E. Şimşek, “On a New Type of q-Baskakov Operators”, SDÜ Fen Bil Enst Der, c. 22, sy. 1, ss. 121–125, 2018, doi: 10.19113/sdufbed.29379.
ISNAD Şimşek, Ersin. “On a New Type of Q-Baskakov Operators”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22/1 (Nisan 2018), 121-125. https://doi.org/10.19113/sdufbed.29379.
JAMA Şimşek E. On a New Type of q-Baskakov Operators. SDÜ Fen Bil Enst Der. 2018;22:121–125.
MLA Şimşek, Ersin. “On a New Type of Q-Baskakov Operators”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 22, sy. 1, 2018, ss. 121-5, doi:10.19113/sdufbed.29379.
Vancouver Şimşek E. On a New Type of q-Baskakov Operators. SDÜ Fen Bil Enst Der. 2018;22(1):121-5.

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