Abstract
It is proved that the Chebyshev polynomial\(\overline T _n (x) = T_n (x\cos \tfrac{\pi }{{2n}})\), has the greatest uniform norm on [−1, 1] of its third derivative among the real polynomials of degree at most n, which are bounded by 1 in [−1, 1] and vanish in −1 and 1.
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Research Supported by the Sofia University Science Foundation under Project No. 153/95.
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Milev, L. An inequality of Schur's type. Approx. Theory & its Appl. 14, 56–63 (1998). https://doi.org/10.1007/BF02836929
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DOI: https://doi.org/10.1007/BF02836929