We construct a piecewise differentiable function that is not piecewise analytic and satisfies a Jackson type estimate for approximation by Lagrange interpolating polynomials associated with the extremal points of the Chebyshev polynomials.
@article{bwmeta1.element.bwnjournal-article-cmv75z1p1bwm, author = {S. Zhou}, title = {On approximation by Lagrange interpolating polynomials for a subset of the space of continuous functions}, journal = {Colloquium Mathematicae}, volume = {78}, year = {1998}, pages = {1-5}, zbl = {0896.41001}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv75z1p1bwm} }
Zhou, S. On approximation by Lagrange interpolating polynomials for a subset of the space of continuous functions. Colloquium Mathematicae, Tome 78 (1998) pp. 1-5. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv75z1p1bwm/
[000] [MS] G. Mastroianni and J. Szabados, Jackson order of approximation by Lagrange interpolation, in: Proc. Second Internat. Conf. in Functional Analysis and Approximation Theory (Aquafredda di Maratea, 1992), Rend. Circ. Mat. Palermo (2) Suppl. 1993, no. 33, 375-386. | Zbl 0837.41003
[001] [Li] X. Li, On the Lagrange interpolation for a subset of C^k functions, Constr. Approx. 11 (1995), 287-297. | Zbl 0830.41001