ON 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, phi-n-->0 + (n --> infinity), 0 < alpha less-than-or-equal-to 2 and [GRAPHICS] for some constrant C > 0. Then for any f epsilon C[-2a, 2a], [GRAPHICS] implies f epsilon Lip*a, where [GRAPHICS] Then some similar results on C2-pi are given, and further some results on C[-2a, 2a] are established by adding some proper conditions.