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Approximation by q-Szász-Mirakyan-Baskakov operators

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EN
In the present paper we propose the q analogue of well known Szász-Mirakyan-Baskakov operators (see e.g. [14], [7]). We apply q-derivatives, and q-Beta functions to obtain the moments of the q-Szász-Mirakyan-Baskakov operators. Here we estimate some direct approximation results for these operators.
Rocznik
Tom
Strony
35--48
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
  • School of Applied Sciences Netaji Subhas Institute of Technology Sector 3 Dwarka, New Delhi 110078 India
autor
  • Kirikalle University Faculty of Science and Arts Department of Mathematics Yahsihan, Turkey
autor
  • Kirikalle University Faculty of Science and Arts Department of Mathematics Yahsihan, Turkey
Bibliografia
  • [1] Agratini O., Dogru O., Weighed approximation by q-Szasz-King type operators, Taiwanese J. Math., 14(2010), 1283-1296.
  • [2] Aral a., A generalization of Szasz Mirakyan operators based on q-integers, Math. Comput. Model., 47(2008), 1052-1062.
  • [3] Aral A., Gupta V., On the Durrmeyer type modification of the q-Baskakov type operators, Nonlinear Analysis, 72(2010), 1171-1180.
  • [4] Aral A., Gupta V., The q-derivative and applications to q-Szasz Mirakyan operators, Calcolo, 43(3)(2006), 151-170.
  • [5] DeVore R.A., Lorentz G.G., Constructive Approximation, Springer, Berlin, (1993).
  • [6] Gasper G., Rahman M., Basic Hypergeometrik Series, Encyclopedia of Mathematics and its Applications, Vol 35, Cambridge University Press, Cambridge, UK, 1990.
  • [7] Gupta V., A note on modified Szasz operators, Bull. Inst. Math. Acad. Sinica, 21(3)(1993), 275-278.
  • [8] Gupta V., Aral A., Convergence of the q-analogue of Szasz Beta operators, Applied Mathematics and Computation, 216(2010), 374-380.
  • [9] Gupta V., Heping W., The rate of convergence of q-Durrmeyer operators for 0 < q < 1, Math. Methods Appl. Sci., 31(16)(2008), 1946-1955.
  • [10] Kac V.G., Cheung P., Quantum Calculus, Universitext, Springer-Verlag, New York, (2002).
  • [11] Koornwinder T.H., q-Special Functions, a Tutorial, in: M. Gerstenhaber, J. Stasheff (Eds), Deformation Theory and Quantum Groups with Applications to Mathematical Physics, Contemp. Math., 134 (1992), Amer. Math.Soc. 1992.
  • [12] Mahmudov N.I., On q-parametric Szasz-Mirakjan operators, Mediterr J. Math., 7(3)(2010), 297-311.
  • [13] Mahmudov N.I., Kaffaoglu H., On q-Szasz-Durrmeyer operators, Central Eur. J. Math., 8(2)(2010), 399-409.
  • [14] Prasad G., Agrawal P.N., Kasana H.S., Approximation of functions on [0, to] by a new sequence of modified Szasz operators, Math. Forum, 6(2)(1983), 1-11.
  • [15] Radu C., Taraibe S., Veteleanu A., On the rate of convergence of a new q-Szasz-Mirakjan operators, Stud. Univ. Babes-Bolyai Math., 56(2)(2011), 527-535.
  • [16]. De Sole A., Kac V.G., On integral representation of q-gamma and q-beta functions, AttiAccad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 16(1)(2005), 11-29.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-3f6aa991-252b-42a2-b71e-08a3de5166ad
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