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Inequalities of Bernstein-Mordell Type

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Inequalities Involving Functions and Their Integrals and Derivatives

Part of the book series: Mathematics and Its Applications ((MAEE,volume 53))

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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

$$\int\limits_{ - 1}^{ + 1} {{{({a_0} + {a_1}x + \cdots + {a_n}{x^n})}^2}dx} \geqslant \frac{2}{{(n + 1)2}}.$$
(1.1)

Except for an obvious error, this relation has been obtained by S. N. Bernstein [1].

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Authors and Affiliations

  1. University of Belgrade, Yugoslavia

    D. S. Mitrinović

  2. University of Zagreb, Yugoslavia

    J. E. Pečarić

  3. Iowa State University, Ames, USA

    A. M. Fink

Authors
  1. D. S. Mitrinović
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  2. J. E. Pečarić
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  3. A. M. Fink
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© 1991 Springer Science+Business Media Dordrecht

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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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  • DOI: https://doi.org/10.1007/978-94-011-3562-7_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5578-9

  • Online ISBN: 978-94-011-3562-7

  • eBook Packages: Springer Book Archive

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