Dual Smale's mean value conjecture

Aimo Hinkkanen; Ilgiz R. Kayumov; Diana M. Khammatova

doi:10.1090/proc/14639

Dual Smale's mean value conjecture

Aimo Hinkkanen, Ilgiz R. Kayumov, Diana M. Khammatova

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the dual Smale's mean value conjecture for polynomials of degree six: if f is a polynomial of degree six with f(0) = 0 and f′(0) = 1, then there is a point ζ such that f′(ζ) = 0 and |f(ζ)/ζ| ≥ 1/6.

Original language	English (US)
Pages (from-to)	5227-5237
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	12
DOIs	https://doi.org/10.1090/proc/14639
State	Published - 2019

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General Mathematics
Applied Mathematics

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title = "Dual Smale's mean value conjecture",

abstract = "We prove the dual Smale's mean value conjecture for polynomials of degree six: if f is a polynomial of degree six with f(0) = 0 and f′(0) = 1, then there is a point ζ such that f′(ζ) = 0 and |f(ζ)/ζ| ≥ 1/6.",

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AU - Khammatova, Diana M.

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AB - We prove the dual Smale's mean value conjecture for polynomials of degree six: if f is a polynomial of degree six with f(0) = 0 and f′(0) = 1, then there is a point ζ such that f′(ζ) = 0 and |f(ζ)/ζ| ≥ 1/6.

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Dual Smale's mean value conjecture

Abstract

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