International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 2, Pages 209-216
doi:10.1155/S0161171294000323
On a subclass of C1 functions for which the Lagrange interpolation yields the Jackson order of approximation
Department of Mathematics, University of Central Florida, Orlando 32816, FL, USA
Received 4 November 1992; Revised 8 January 1993
Copyright © 1994 Xin Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We continue the investigation initiated by Mastroianni and Szabados on 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 C1 functions the local order of approximation given by Lagrange interpolation can be much better (of at least O(1n)) than Jackson's order.