Li, Xin On a subclass of \(C^ 1\) functions for which the Lagrange interpolation yields the Jackson order of approximation. (English) Zbl 0793.41005 Int. J. Math. Math. Sci. 17, No. 2, 209-216 (1994). 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. MSC: 41A05 Interpolation in approximation theory 41A25 Rate of convergence, degree of approximation Keywords:Jackson’s order of approximation; Lagrange interpolation PDFBibTeX XMLCite \textit{X. Li}, Int. J. Math. Math. Sci. 17, No. 2, 209--216 (1994; Zbl 0793.41005) Full Text: DOI EuDML