Yıl 2018, Cilt 22, Sayı 1, Sayfalar 121 - 125 2018-03-29

On a New Type of q-Baskakov Operators

Ersin ŞİMŞEK [1]

402 102

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.
q-Analysis, Korovkin's theorem; Baskakov operators
  • [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.
  • [3] Kac, V., Cheung, P. 2002. Quantum Calculus. Universitext Springer-Verlag New York, 112s.
  • [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.
  • [6] Phillips, G. M. 1997. Bernstein polynomials based on the q-integers. Annals of Numerical Mathematics, 4(1997), 511-518.
  • [7] Heping, W. 2008. Properties of convergence for w;q-Bernstein polynomials. Journal of Mathematical Analysis and Applications, 340(2)(2008), 1096-1108.
  • [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.
  • [10] Ostrovska, S. 2003. q-Bernstein polynomials and their iterates. Journal of Approximation Theory, 123(2003), 232-255.
  • [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.
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Yazar: Ersin ŞİMŞEK

Bibtex @ { sdufenbed425678, journal = {Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi}, issn = {}, eissn = {1308-6529}, address = {Süleyman Demirel Üniversitesi}, year = {2018}, volume = {22}, pages = {121 - 125}, doi = {10.19113/sdufbed.29379}, title = {On a New Type of q-Baskakov Operators}, key = {cite}, author = {ŞİMŞEK, Ersin} }
APA ŞİMŞEK, E . (2018). On a New Type of q-Baskakov Operators. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22 (1), 121-125. Retrieved from http://dergipark.gov.tr/sdufenbed/issue/37055/425678
MLA ŞİMŞEK, E . "On a New Type of q-Baskakov Operators". Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 (2018): 121-125 <http://dergipark.gov.tr/sdufenbed/issue/37055/425678>
Chicago ŞİMŞEK, E . "On a New Type of q-Baskakov Operators". Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 (2018): 121-125
RIS TY - JOUR T1 - On a New Type of q-Baskakov Operators AU - Ersin ŞİMŞEK Y1 - 2018 PY - 2018 N1 - DO - T2 - Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi JF - Journal JO - JOR SP - 121 EP - 125 VL - 22 IS - 1 SN - -1308-6529 M3 - UR - Y2 - 2018 ER -
EndNote %0 Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi On a New Type of q-Baskakov Operators %A Ersin ŞİMŞEK %T On a New Type of q-Baskakov Operators %D 2018 %J Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi %P -1308-6529 %V 22 %N 1 %R %U
ISNAD ŞİMŞEK, Ersin . "On a New Type of q-Baskakov Operators". Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 / 1 (Mart 2018): 121-125.