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Rate of convergence of Szász-beta operators based on q-integers

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EN
Abstrakty
EN
The purpose of this paper is to establish the rate of convergence in terms of the weighted modulus of continuity and Lipschitz type maximal function for the q-Szász-beta operators. We also study the rate of A-statistical convergence. Lastly, we modify these operators using King type approach to obtain better approximation.
Wydawca
Rocznik
Strony
130--143
Opis fizyczny
Bibliogr. 31 poz.
Twórcy
autor
  • Department of Mathematics, IIT Roorkee, India
  • Department of Mathematics, IIT Roorkee, India
Bibliografia
  • [1] Lupas A., A q-analogue of the Bernstein operator, In: Seminar on Numerical and Statistical Calculus (Cluj-Napoca, 1987), Univ. ‘Babeş-Bolyai’, Cluj-Napoca, 1987, 9, 85-92
  • [2] Phillips G. M., Bernstein polynomials based on the q-integers, The heritage of P. L. Chebyshev: a Festschrift in honour of the 70th birthday of Prof. T. J. Rivlin. Ann. Numer. Math., 1997, 4(1-4), 511-518
  • [3] Aral A., A generalization of Szász-Mirakyan operators based on q-integers, Math. Comput. Model., 2008, 47(9), 1052-1062
  • [4] Aral A., Gupta V., The q-derivative and applications to q-Szász Mirakyan operators, Calcolo, 2006, 43(3), 151-170
  • [5] Gupta V., Mahmudov N. I., Approximation properties of the q-Szász-Mirakyan-beta Operators, Ind. J. Indus. Appl. Math., 2012, 3(2), 41-53
  • [6] Gupta V., Aral A., Convergence of the q analogue of Szász-Beta operators, Appl. Math. Comput., 2010, 216(2), 374-380
  • [7] Örkcü M., Doğru O., q-Szász-Mirakjan Kantorovich type operators preserving some test functions, Appl. Math. Lett., 2011, 24(9), 1588-1593
  • [8] Gupta V., Srivastava G. S., Sahai A., On simultaneous approximation by Szász-beta operators, Soochow J. Math., 1995, 21(1), 1-11
  • [9] Yüksel I., Dinlemez U., Voronovskaja type approximation theorem for q-Szász-beta operators, Appl. Math. Comp., 2014, 235, 555-559
  • [10] Aral A., Gupta V., Agarwal R. P., Applications of q-Calculus in Operator Theory, Berlin: Springer, 2013
  • [11] Gupta V., Agarwal R. P., Convergence estimates in approximation theory, Berlin: Springer, 2014
  • [12] Kac V., Cheung P., Quantum calculus, Springer, New York, 2002
  • [13] Özarslan M. A., Duman O., Local approximation behaviour of modied SMK operators, Miskolc Math. Notes, 2010, 11(1), 87-99
  • [14] Erençin A., Durrmeyer type modication of generalized Baskakov operators, Appl. Math. Comput., 2003, 218(8), 4384-4390
  • [15] Agratini O., Doğru O., Weighted approximation by q-Szász-King type operators, Taiwanese J. Math., 2010, 14(4), 1283
  • [16] Erençin A., Bascanbaz-Tunca G., Approximation properties of a class of linear positive operators in weighted spaces, Cr. Acad. Bulg. Sci., 2010, 63(10), 1397-1404
  • [17] Agrawal P. N., Karsli H., and Goyal M. , Szász-Baskakov type operators based on q-integers, J. Inequal Appl. 2014, 2014, 1-18.
  • [18] Lopez-Moreno A. J., Weighted simultaneous approximation with Baskakov type operators, Acta Math. Hung., 2004, 104(1-2), 143-151
  • [19] Lenze B., On Lipschitz type maximal functions and their smoothness spaces, Indag. Math., 1988, 50(1), 53-63
  • [20] Kolk E., Matrix summability of statistically convergent sequences, Analysis, 1993, 13(1-2), 77-83
  • [21] Ersan S., Doğru O., Statistical approximation properties of q-Bleimann, Butzer and Hahn operators, Math. Comput. Modelling, 2009, 49(7), 1595-1606
  • [22] Gadjiev A. D., Orhan C., Some approximation theorems via statistical convergence, J. Math., 2002, 32(1)
  • [23] Gupta V., Radu C., Statistical approximation properties of q-Baskakov-Kantorovich operators, Cent. Eur. J. Math., 2009, 7(4), 809-818
  • [24] Ispir N., Gupta V., A-Statistical approximation by the generalized Kantorovich-Bernstein type rational operators, Southeast Asian Bull. Math., 2008, 32, 87-97
  • [25] Örkcü M., Doğru O., Statistical approximation of a kind of Kantorovich type q-Szász-Mirakjan operators, Nonlinear Anal., 2012, 75(5), 2874-2882
  • [26] Örkcü M., Doğru O., Weighted statistical approximation by Kantorovich type q-Szász-Mirakjan operators, Appl. Math. Comput., 2011, 217(20), 7913-7919
  • [27] Ünal Z., Özarslan M. A., Duman O., Approximation properties of real and complex Post-Widder operators based on q-integers, Miskolc Math Notes, 2012, 13, 581-603
  • [28] Duman O., Orhan C., Statistical approximation by positive linear operators, Stud. Math., 2004, 161(2), 187-197
  • [29] Duman O., Khan M. K., Orhan C., A-statistical convergence of approximating operators, Math. Inequal. Appl., 2003, 6(4), 689-699
  • [30] King J. P., Positive linear operators which preserve x2, Acta Math. Hung., 2003, 99(3), 203-208
  • [31] DeVore R.A., Lorentz G.G., Constructive Approximation, Springer, Berlin 2013
Uwagi
PL
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
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Bibliografia
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