OM AN INVERSE THEOREM OF APPROXIMATION

The author gives some disagreement to the following result, which is published in [1].Let ${L_{n}(f)}$ be mass-concerntative,$phirightarrow 0(nrightarrow infty), 00$. Then for any $fin C[-2a,2a]$, $$parallel L_{n}(f)-fparallel_{C[ a,a]}= O(phi^{alpha}_{n})$$inplies $f in Lip^{*}alpha$, where$$Lip*alpha={fin C[-2a,2a]|omega_{2}(f,delta)_{[-2a,2a]}=O(delta^{alpha})}.$$Then some similar results on $C_{2pi$ are given, and further some results on $C[-2a,2a]$ are established by adding some proper conditions.