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Mean convergence of Hermite-Fejér type interpolation on an arbitrary system of nodes

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Analysis in Theory and Applications

Abstract

In this paper sufficient conditions for mean convergence and rate of convergence of Hermite-Fejér type interpolation in the Lp norm on an arbitrary system of nodes are presented.

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References

  1. Szabados, J. and Varma, A. K., On Higher Order Hermite-Fejér Interpolation in WeightedL p—Metric, Acta Math. Hungar., 59(1991), 133–140.

    Article  MathSciNet  Google Scholar 

  2. Erdës, P., On the Uniform Distribution of the Roots of Certain Polynomials, Ann. of Math., 43(1942), 59–64.

    Article  MathSciNet  Google Scholar 

  3. Vértesi, P. and Xu, Y., Truncated Hermite Interpolation Polynomials, Studia Sci. Hungar., 28(1993), 205–213.

    MATH  Google Scholar 

  4. Shi, Y. G., Mean Convergence of Lagarange Type Interpolation on an Arbitrary System of Nodes, Acta Math. Appl. Sinica., to appear.

  5. Shi, Y. G., Mean Convergence of Truncated Hermite Interpolation on an Arbitrary System of Nodes, Acta Math. Hungar., 76(1997), 45–58.

    Article  MATH  MathSciNet  Google Scholar 

  6. Shi, Y. G., On Hermite Interpolation, J. Approx. Theory, 105(2000), 49–86.

    Article  MATH  MathSciNet  Google Scholar 

  7. Shi, Y. G., Mean Convergence of Interpolatory Processes on Arbitrary System of Nodes, Acta Math. Hungar., 70(1996), 27–38.

    Article  MATH  MathSciNet  Google Scholar 

  8. Shi, Y. G., Mean Convergence of Hermite Interpolation of High Order on an Arbitrary System of Nodes, Submitted to J. Math. Rearch Expos., to appear.

  9. Shi, Y.G., Truncated Hermite Interpolation on an Arbitrary System of Nodes, J. Approx. Theory., to appear.

  10. Shi, Y. G., Necessary Condition for Mean Convergence of Lagrange Interpolation on an Arbitrary System of Nodes, Acta Math. Hungar., 72(1996), 251–260.

    Article  MATH  MathSciNet  Google Scholar 

  11. Ditzian, Z. and Totik, V., Moduli of Smoothness, Springer Series in Computational Mathematics, Vol. 9, Springer-Verlag, New York-Berlin, 1987.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics School of Science, Guangzhou University, 510405, Guangzhou, P. R. China

    Feng Yongping

  2. CAS, Academy of Mathematics and System Science, 100080, Beijing, P. R. China

    Feng Yongping

  3. Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Science, Academy of Chinese Science, P.O. Box 2719, 100080, Beijing, P. R. China

    Cui Junzhi

Authors
  1. Feng Yongping
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  2. Cui Junzhi
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Corresponding author

Correspondence to Feng Yongping.

Additional information

Project 19671082 supported by National Natural Science Foundation of China, I acknowledge endless help from Prof. Shi Ying-Guang during finishing this paper.

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Yongping, F., Junzhi, C. Mean convergence of Hermite-Fejér type interpolation on an arbitrary system of nodes. Anal. Theory Appl. 20, 199–214 (2004). https://doi.org/10.1007/BF02835289

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  • DOI: https://doi.org/10.1007/BF02835289

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