On a subclass of \(C^ 1\) functions for which the Lagrange interpolation yields the Jackson order of approximation (Q1326603)

Summary: We continue the investigation initiated by Mastroianni and Szabados on the question whether Jackson's order of approximation can be attained by Lagrange interpolation for a wide class of functions. Improving a recent result of Mastroianni and Szabados, we show that for a subclass of \(C^ 1\) functions the local order of approximation given by Lagrange interpolation can be much better (of at least \(O({1 \over n}))\) than Jackson's order.