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The convergence rate of Multi-Bernstein-Durrmeyer operators with Jacobi weights

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Approximation Theory and its Applications

Abstract

In this paper, we will consider the convergence rate of Multi-Bernstein-Durrmeyer operators with Jacobi weights and characterizations of approximation rate by means of a new K-functional.

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References

  1. Ditzian, Z. and Ivanov, K., Bernstein-Type Operators and Their Derivations, J. Approx. Theory, 56(1989), 72–89.

    Article  MATH  MathSciNet  Google Scholar 

  2. Zhang, Z. Q., On Weight Approximation of Bernstein Operators, Approx. Theory and Its Appli., 9(1993), No. 3, 61–72.

    Google Scholar 

  3. Heilmann, M.,L p-Satoration of Some Modified Bernstein Operators, J. Approx. Theory, 53 (1988), 260–273.

    Article  MathSciNet  Google Scholar 

  4. Ditzian, Z. and Totik, V., Moduli of Smoothness, Speringer, 1987.

  5. Grundmann, A., Inverse Theorem for Kanotorovich Polynomials, in “Fourier Analysis and Approximation Theory”, North-Holland, Amsterdam, 1978, 395–401.

    Google Scholar 

  6. Zhou, D. X., Inverse Theorem for Multidimensional Bernstein-Durrmeyer Operators inL p J. Approx. Theory, 70(1992), 68–93.

    Article  MATH  MathSciNet  Google Scholar 

  7. Xuan, P. C., On Weighted Approximation for a Class of Multidimensional Linear Positive Operators inL p, Acta Math. Appl. Sinica, 19(1996), No. 3, 370–384.

    MathSciNet  Google Scholar 

  8. Xuan, P. C., On Weighted Approximation by Baskakov Type Operators, China Anna Math., 16A:5(1995), 614–624.

    MathSciNet  Google Scholar 

  9. Xuan, P. C., On Weighted Approximation by Szász-Mirakjan Type Operators, Math. Num. Sinica, 4(1995), 427–442.

    MathSciNet  Google Scholar 

  10. Xuan, P. C. and Zhou, D. X., Rate of Convergence for Baskakov Operators with jacobi-Weights, Acta Math. Appl. Sinics, 18(1995), No. 1, 129–139.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Shaoxing College of Arts and Sciences, 312000, Shaoxing, Zhejiang, PRC

    Xuan Peicai, Wang Jianli & You Gongqiang

  2. Department of Mathematics, Zhejiang University, 310027, Hangzhou, Zhejiang, PRC

    Song Ruying

Authors
  1. Xuan Peicai
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  2. Wang Jianli
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  3. You Gongqiang
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  4. Song Ruying
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Peicai, X., Jianli, W., Gongqiang, Y. et al. The convergence rate of Multi-Bernstein-Durrmeyer operators with Jacobi weights. Approx. Theory & its Appl. 18, 90–101 (2002). https://doi.org/10.1007/BF02837405

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  • DOI: https://doi.org/10.1007/BF02837405

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