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| OM AN INVERSE THEOREM OF APPROXIMATION |
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Citation： |
Yang Lihua.OM AN INVERSE THEOREM OF APPROXIMATION[J].Chinese Annals of Mathematics B,1991,12(2):219~229 |
| Page view： 833
Net amount： 963 |
Authors： |
Yang Lihua; |
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| Abstract： |
The author gives some disagreement to the following result, which is published in [1].
Let ${L_{n}(f)}$ be mass-concerntative,$\phi\rightarrow 0(n\rightarrow \infty), 0<\alpha\leq2$ and
$$C^{-1}\leq \phi_{n+1}/\phi_{n}\leq C (n=1,2,\ldots)$$
for some constrant $C>0$. Then for any $f\in C[-2a,2a]$,
$$\parallel L_{n}(f)-f\parallel_{C[ a,a]}= O(\phi^{\alpha}_{n})$$
inplies $f \in Lip^{*}\alpha$, where
$$Lip*\alpha={f\in C[-2a,2a]|\omega_{2}(f,\delta)_{[-2a,2a]}=O(\delta^{\alpha})}.$$
Then some similar results on $C_{2\pi$ are given, and further some results on $C[-2a,2a]$ are established by adding some proper conditions. |
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