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ON CERTAIN PROPERTIES OF THE COMBINATIONS OF SZáSZ-DURRMEYER OPERATORS

ON CERTAIN PROPERTIES OF THE COMBINATIONS OF SZáSZ-DURRMEYER OPERATORS
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摘要 In the present paper we study properties of Szaisz-Durrmeyer operators. These operators are introduced in [5] and generalize the integral operators proposed by S.M.Mazhar and V.Totik in [ 12]. We also generalize some results obtained by M. Heilmann[6] and D.-X. Zhou[16]. In the present paper we study properties of Szaisz-Durrmeyer operators. These operators are introduced in [5] and generalize the integral operators proposed by S.M.Mazhar and V.Totik in [ 12]. We also generalize some results obtained by M. Heilmann[6] and D.-X. Zhou[16].
作者 Tomasz Swiderski
机构地区 Pedagogical University
出处 《Analysis in Theory and Applications》 2011年第2期167-180,共14页 分析理论与应用（英文刊）
关键词 modified Szasz-Mirakyan operator Baskakov-Durremeyer operator modified Szasz-Mirakyan operator, Baskakov-Durremeyer operator
分类号 O177 [理学—基础数学]
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参考文献16

  • 1Berens, H. and Lorentz, G.G., Inverse Theorems for Bernstein Polynomials, Indiana Univ. Math. J., 21(1972), 693-708.
  • 2Butzer, E L., Linear Combinations of Bemstein Polynomials, Can. J. Math., 5(1953), 559-567.
  • 3Ditzan, Z., Global Inverse Theorem for Combinations of Bemstein Polynonaials, J. Approx. Theory, 26(1979), 277-292.
  • 4Ditzan, Z. and Totik, V., Moduli of Smoothness, Springer Series in Computational Mathematics, 9 Springer- Verlag.
  • 5Ciupta, A. and Gavrea, I., On a Modified Favard-Szasz Operator, Univ. Babes-Bolyai, Cluj-Napoca, Faculty of Math. and Informatics Research Seminars, Seminar on Numerical and Statistical Calculus, 1 (1994), 39-44.
  • 6Heilmann, M., Operators of Baskakov-Durrmeyer type, Approx. Theory and its Appl., 5:1 Mar. (1989).
  • 7Gonska, H. H. and Zhou, D. X., Local Smoothness of Functions and Bernstein-Durrmeyer Operators, Com- puters Math. Applic., 30:3-6(1995), 83-101.
  • 8Guo, S., Li, C., Sun, Y., Yang, G. and Yue, S., Pointwise Estimate for Szasz-Type Operators, J. Approx. Theory, 94(1998), 160-171.
  • 9Lu, C. B. and Xie, L. S., The Lp-saturation for Linear Combination of Berenstein-Kantorovich Operators, Acta Math. Hungar., 120:4(2008), 367-381.
  • 10May, C. P., Saturation and Inverse Theorems for Combinations of Bemstein-type Operators, Thesis 1974, University of Alberta.
Analysis in Theory and Applications
2011年 第2期

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