Abstract
In this paper the order of bestapproximation by algebraic polynomials is related to the order of weighted simultaneous approximation. A special case of a Markov-Bernstein type inequality proved by Ditzian and Totik in a very general fashion is used.
Similar content being viewed by others
References
P. L. Butzer, K. Scherer (1969): Über die Fundamentals ätze der klassischen Approximationstheorie in abstrakten Räumen. In: Proc. of the Conf. at Math. Res. Inst. Oberwolfach July 18–27, 1968, P. L. Butzer, B. Sz. Nagy (eds.), ISNM 10, Basel, Birkhäuser Verlag, pp. 113–125.
Z. Ditzian, V. Totik (1987): Moduli of Smoothness. Berlin, Heidelberg, New York: Springer Verlag (Springer Series in Computational Mathematics 9).
S. B. Steckin (1951): On the order of the best approximation of continuous functions. Izv. Akad. Nauk SSSR (seriya mat.), 15: 219–242.
A. F. Timan (1963): Theory of Approximation of Functions of a Real Variable. New York: Pergamon Press.
M. Zamansky (1949): Classes de saturation de certains procédés d’approximation des séries de Fourier et application à quelques problèmes d’approximation. Ann. Sci. École Norm. Sup., 66: 19–93.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Heilmann, M. On Simultaneous Approximation by Optimal Algebraic Polynomials. Results. Math. 16, 77–81 (1989). https://doi.org/10.1007/BF03322645
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03322645