Periodica Mathematica Hungarica

, Volume 9, Issue 3, pp 249–254 | Cite as

On the divergence of certain Hermite-Fejér interpolation

  • P. Vértesi
Article
  • 15 Downloads

Summary

In his paper [1]P. Turán discovers the interesting behaviour of Hermite-Fejér interpolation (based on the Čebyšev roots) not describing the derivative values at “exceptional” nodes {ηn} n=1 . Answering to his question we construct such exceptional node-sequence for which the mentioned process is bounded for bounded functions whenever −1<x<1 but does not converge for a suitable continuous function at any point of the whole interval [−1, 1].

AMS (MOS) subject classifications (1970)

Primary 41A05 41A10 41A25 

Key words and phrases

Hermite Fejér interpolation positive operators 

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References

  1. [1]
    P. Turán, A remark on Hermite—Fejér interpolation,Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 3–4 (1960–61), 369–377.MR 25#370Google Scholar
  2. [2]
    P. Turán, Az approximációelmélet egyes nyitott problémáiról (On some unsolved problems in approximation theory),Mat. Lapok 25 (1974), 21–75. (In Hungarian)Google Scholar
  3. [3]
    P. Vértesi, On a problem of P. Turán,Canad. Math. Bull. 18 (1975), 283–288.MR 52#14751Google Scholar

Copyright information

© Akadémiai Kiadó 1978

Authors and Affiliations

  • P. Vértesi
    • 1
  1. 1.MTA Matematikai Kutató IntézetBudapestHungary

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