Periodica Mathematica Hungarica

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

On the divergence of certain Hermite-Fejér interpolation

  • P. Vértesi


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 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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

Personalised recommendations