On critical values of polynomials with real critical points

Aimo Hinkkanen, Ilgiz Kayumov

Research output: Contribution to journalArticlepeer-review


Let f be a polynomial of degree at least 2 with f(0)=0 and f′(0)=1. Suppose that all the zeros of f′ are real. We show that there is a zero ζ of f′ such that {pipe} f(ζ)/ζ{pipe} ≤ 2/3, and that this inequality can be taken to be strict unless f is of the form f(z)=z+cz3.

Original languageEnglish (US)
Pages (from-to)385-392
Number of pages8
JournalConstructive Approximation
Issue number2
StatePublished - 2010


  • Critical points
  • Critical values
  • Polynomials
  • Smale's conjecture

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Computational Mathematics


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