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The Simultaneous Approximation Order by Hermite Interpolation in a Smooth Domain

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Abstract

Let D be a smooth domain in the complex plane. In D consider the simultaneous approximation to a function and its ith (0 ≤i≤q) derivatives by Hermite interpolation. The orders of uniform approximation and approximation in the mean, are obtained under some domain boundary conditions. Some known results are included as particular cases of the theorems of this paper.

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Authors and Affiliations

  1. Department of Information Engineering, North China Institute of Hydroelectricity, Zhengzhou, 450045, P. R. China

    Tian Liang Tu

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  1. Tian Liang Tu
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Correspondence to Tian Liang Tu.

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Supported by NSF of Henan Province (974050900)

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Tu, T.L. The Simultaneous Approximation Order by Hermite Interpolation in a Smooth Domain. Acta Math Sinica 18, 631–646 (2002). https://doi.org/10.1007/s10114-002-0202-x

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  • DOI: https://doi.org/10.1007/s10114-002-0202-x

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