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A partial answer to a conjecture of Szabados. (English) Zbl 0924.41004
This paper proves a result: Suppose that \(X\) is strongly normal and \(\overline X=[-1,1]\). If \(f\in C[-1,1]\) satisfies \(\| H_n(X,f)-f\| =\circ (n^{-1})\) then \(f=constant\), where \(H_n(X,f)\) is the Hermite approximation interpolation of \(f\) on the nodes \(X\). But this result is only a direct consequence of Theorem 8 in Reference [3] of the paper ([Some notes on Hermite-Fejér type interpolation, Approximation Theory Appl. 7, No. 4, 28-39 (1991; Zbl 0757.41006)] given by the reviewer.
MSC:
41A05 Interpolation in approximation theory
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