Abstract
In this note we obtain error bounds to τx2n+1−σx2n on [−1, 1] by polynomials of degree at most (2n−1). The result proved here improves and extends some of the known results of Zolotarev and Bernstein. The proof presented here is different (and simple) from the one adopted by Zolotarev and Bernstein.
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References
ACHIESER, N.: Theory of Approximation. New York: Frederick Ungar Publishing Co. 1956.
BERNSTEIN, S. N.: Collected Works, Vol. 1, Constructive Theory of Functions (1905–1930). U. S. Atomic Energy Commission, AEC-tr-3460, Technical Information Service Extension, Oak Ridge, Tennessee.
TIMAN, A. F.: Theory of Approximation of Functions of a Real Variable. New York: Pergamon Press, 1963.
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Reddy, A.R. A note on a result of Zolotarev and Bernstein. Manuscripta Math 20, 95–97 (1977). https://doi.org/10.1007/BF01181242
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DOI: https://doi.org/10.1007/BF01181242