Abstract
Pointwise and uniform bounds are determined for the derivatives of real algebraic polynomials p(x) which on the interval [−1,1] satisfy (1−x2)λ/2|p(x)| ≤ 1, λ a fixed positive integer. The pointwise bounds are investigated with regard to their sharpness while the uniform bounds are shown to be best possible in an asymptotic sense.
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References
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© 1984 Springer-Verlag
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Lachance, M.A. (1984). Bernstein and markov inequalities for constrained polynomials. In: Graves-Morris, P.R., Saff, E.B., Varga, R.S. (eds) Rational Approximation and Interpolation. Lecture Notes in Mathematics, vol 1105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072405
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DOI: https://doi.org/10.1007/BFb0072405
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