Abstract
If a real polynomial f n(x=a 0+a 1 x+...+a n x n reaches the value of 1 anywhere on the segment [-1,1], then
Except for an obvious error, this relation has been obtained by S. N. Bernstein [1].
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References
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Mitrinović, D.S., Pečarić, J.E., Fink, A.M. (1991). Inequalities of Bernstein-Mordell Type. In: Inequalities Involving Functions and Their Integrals and Derivatives. Mathematics and Its Applications, vol 53. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3562-7_16
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