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Proof of a polynomial conjecture


Author: G. K. Kristiansen
Journal: Proc. Amer. Math. Soc. 44 (1974), 58-60
MSC: Primary 26A75; Secondary 42A04
DOI: https://doi.org/10.1090/S0002-9939-1974-0340516-4
Erratum: Proc. Amer. Math. Soc. 58 (1976), 377.
MathSciNet review: 0340516
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Abstract | References | Similar Articles | Additional Information

Abstract: Let a real polynomial have only real roots, all belonging to an interval $ I$. An inequality is proved, relating the average value of the polynomial between two consecutive roots to its maximal absolute value in $ I$.


References [Enhancements On Off] (What's this?)

  • [1] P. Erdös, Note on some elementary properties of polynomials, Bull. Amer. Math. Soc. 46 (1940), 954-958 (see p. 957). MR 2, 242. MR 0003595 (2:242b)
  • [2] P. Erdös and T. Grünwald (Gallai), On polynomials with only real roots, Ann. Math. 40 (1939), 537-548 (see p. 538). MR 1, 1. MR 0000007 (1:1g)

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DOI: https://doi.org/10.1090/S0002-9939-1974-0340516-4
Article copyright: © Copyright 1974 American Mathematical Society

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