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Approximation properties of Kantorovich type q-Balázs-Szabados operators

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, we introduce a new kind of q-Balázs-Szabados-Kantorovich operators called q-BSK operators. We give a weighted statistical approximation theorem and the rate of convergence of the q-BSK operators. Also, we investigate the local approximation results. Further, we give some comparisons associated with the convergence of q-BSK operators.
Wydawca
Rocznik
Strony
10--19
Opis fizyczny
Bibliogr. 25 poz., wykr.
Twórcy
  • Gazi University, Faculty of Science, Department of Mathematics, 06500, Ankara/Turkey
Bibliografia
  • [1] Acar T., Quantitative q-Voronovskaya, q-Grüss-Voronovskaya-type results for q-Szasz operators, G. Math. J., 2016, 23(4), 459-468
  • [2] Acar T., (p,q)-Generalization of Szasz-Mirakyan operators, Math. Methods in the Appl. Sciences, Math. Methods in the Appl. Sciences, 2016, 39(10), 2685-2695
  • [3] Acar T., Aral A., Mohiuddine S. A., On Kantorovich modification of (p,q)-Baskakov operators, J. Inequal. Appl., 2016, 98
  • [4] Acar T., Mohiuddine S. A., Mursaleen M., Approximation by (p,q)-Baskakov-Durrmeyer-Stancu operators, Complex Anal. Oper. Theory, 2018, 12(6), 1453-1468
  • [5] Mohiuddine S. A., Acar T., Alotaibi A., Construction of a new family of Bernstein-Kantorovich operators, Math. Meth. Appl. Sci., 2017, 40(18), 7749-7759
  • [6] Mohiuddine S. A., Acar T., Alghamdi A., Genuine modified Bernstein-Durrmeyer operators, J. Inequal. Appl., 2018, 2018:104
  • [7] Bodur M., Yılmaz Ö. G., Aral A., Approximation by Baskakov-Szász-Stancu Operators Preserving Exponential Functions, Constructive Mathematical Analysis, 2018, 1(1), 1-8
  • [8] Doğru O., Duman O., Statistical approximation of Meyer-König and Zeller operators based on q-integers, Publ. Math. Debrecen, 2006, 68(1-2), 199-214
  • [9] Radu C., Statistical approximation properties of Kantorovich operators based on q-integers, Creative Math. Inf., 2008, 17(2), 75-84
  • [10] Ersan S., Doğru O., Statistical approximation properties of q-Bleimann,Butzer and Hahn operators, Math. Comput. Modelling, 2009, 49(7-8), 1595-1606
  • [11] Gupta V., Radu C., Statistical approximation properties of q-Baskokov-Kantrovich operators, Cent. Eur. J. Math., 2009, 7(4), 809-818
  • [12] Dalmanoğlu Ö., Doğru O., On statistical approximation properties of Kantrovich type q-Bernstein operators, Math. Comput. Modelling, 2010, 52(5-6), 760-771
  • [13] Mursaleen M., Khan A., Statistical approximation properties of modifiedq-Stancu-Beta operators, Bull. Malays. Math. Sci. Soc. (2), 2013, 36(3), 683-690
  • [14] Ren M.-Y., Zeng X.-M., Some statistical approximation properties of Kantorovich-type q-Bernstein-Stancu operators, J. Inequal. Appl., 2014, 2014:10
  • [15] Andrews G. E., Askey R., Roy R., Special functions, Cambridge University Press,1999
  • [16] Kac V., Cheung P., Quantum Calculus, Springer-Verlag, Newyork, 2002
  • [17] Aral A., Gupta V., Agarwal R. P., Applications of q-Calculus in Operator Theory, Springer, 2013
  • [18] Balázs K., Approximation by Bernstein type rational function, Acta Math. Acad. Sci. Hungar, 1975, 26(1-2), 123-134
  • [19] Balázs K., Szabados J., Approximation by Bernstein type rational function II, Acta Math. Acad. Sci. Hungar, 1982, 40(3-4), 331-337
  • [20] Doğru O., On statistical approximation properties of Stancu type bivariate generalization of q-Balázs-Szabados operators, In: Proceedings of the International Conference on Numerical Analysis and Approximation Theory, Cluj-Napoca, Romania, 2006, 179-194
  • [21] Ozkan E. Y., An upper estimate of q-Balázs-Szabados-Kantorovich operators on compact disks, G.U. J. Sci., 2016, 29(2), 479-486
  • [22] Fast H., Sur la convergence statistique, Collog. Math., 1951, 2(3-4), 241-244
  • [23] Niven I., Zuckerman H. S., Montgomery H., An Introduction to the Theory of Numbers, 5th edition, Wiley, New York, 1991
  • [24] Lopez-Moreno A-J, Weighted simultaneous approximation with Baskakov type operators, Acta Math. Hungar., 2004, 104(1-2), 143-151
  • [25] De Vore R. A., Lorentz G. G., Constructive approximation, Springer, Berlin, 1993
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-76c220a8-d26f-4869-b8dc-946d568cc770
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