A partial answer to a conjecture of Szabados. (English) Zbl 0924.41004

Wang, Quanlong

J. Math. Study 30, No. 4, 364-366 (1997).

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.

Reviewer: Shi Ying-Guang (Beijing)

MSC:

41A05

Interpolation in approximation theory

Keywords:

Hermite-Fejér interpolation; saturation