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  • 1 Ankara University, Tandogan 06100, Ankara, Turkey
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In this paper we introduced the general sequence of linear positive operators via generating functions. Approximation properties of these operators are obtained with the help of the Korovkin Theorem. The order of convergence of these operators computed by means of modulus of continuity Peetre’s K-furictiorial and the elements of the usual Lipschitz class. Also we introduce the r-th order generalization of these operators and we evaluate this generalization by the operators defined in this paper. Finally we give some applications to differential equations.

  • [1]

    Alkemade, J. A. H., The Second Moment for the Meyer-König and Zeller Operators, J. Approx. Theory 40 (1984), 261273. MR85f:41021

  • [2]

    Bleimann, G., Butzer, P. L. and Hahn, L., A Berristeiri-type operator approximating continuous functions on the semi-axis, NederL Akad, Wetensch Indag, Math, 42 (1980), 255262. MR81mml:41023

    • Search Google Scholar
    • Export Citation
  • [3]

    Cheney, E. W. and Sharma, A., Bernstein power series, Canad. J. Math, 16 (1964), 241252. MR31#3770

  • [4]

    Dogru, Ö., Weighted approximation properties of Szasz-type operators, Intern, Math, J. 2(9) (2002), 889895. MR 1919678

  • [5]

    Dogru, Ö., Approximation order and asymptotic approximation for Generalized Meyer-KÖriig and Zeller operators, Math, Balkanica, N.S” no. 3–4, 12 (1998), 359368. MR2000e:41037

    • Search Google Scholar
    • Export Citation
  • [6]

    Khan, M. K., On the rate of convergence of Bernstein power series for functions of bounded variation, J. Approx, Theory 57 (1989), 90103. MR90d:41043

    • Search Google Scholar
    • Export Citation
  • [7]

    Kirov, G. H. and Popova, L., A generalization of the linear positive operators, Math. Balkanica 7 (1993), 149162. MR95i:41048

  • [8]

    Kirov, G. H., Approximation with Quasi-Spliries, Inst, Physics PubL, Bristol (New York, 1992). MR93f:41001

  • [9]

    May, C. P., Saturation and inverse theorems for combinations of a class of exporieritial- type operators, Canad. J. Math. 28 (1976), 12241250. MR55#8640

    • Search Google Scholar
    • Export Citation
  • [10]

    Meyer-König, W. and Zeller, K., Berristeirische poterizreiheri, Studia Math, 19 (1960), 8994. MR22#2823

  • [11]

    Szasz, O., Generalization of S. Bernstein’s polynomials to the infinite interval, J. Reserarch Nat. Bur. Standards, 45 (1950), 239245. MR13,648c

    • Search Google Scholar
    • Export Citation
  • [12]

    Volkov, Yu.I., Certain positive linear operators, Mat. Zametki, 23 (1978), 363368.