Rational approximation of some limited smooth functions

In this paper, Newman-type rational interpolation to some limited smooth functions induced by some set of nodes X in [−1, 1] is considered and the upper and lower bound of the order of approximation is given, which is sharper than Stahl's result. And the error estimation isCn−α2α+1exp(−nαα+1)≤|en(X;x)|≤3exp(−nαα+1).