Jürgen Prestin, Alina Stosiek
Approximation in Hölder norms with higher order differences
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 51, 33-51(1997)

MSC:

41A05 Interpolation, See also {42A15 and 65D05}

41A10 Approximation by polynomials, {For approximation by trigonometric polynomials, See 42A10}

65D05 Interpolation

Abstract: In this paper we obtain Markov-, Markov-Bernstein- and Jackson-type
estimates in Hölder-norms, where the Hölder-terms are constructed from
first and second order differences. An application to approximation
results for interpolatory processes is outlined.
Keywords: Hölder-Zygmund-norms, Markov-Bernstein-type inequalities, Jackson-type estimates.