Просмотр по автору "Hinkkanen A."

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Dual Smale's mean value conjecture

Hinkkanen A.; Kayumov I.; Khammatova D. (2019)

© 2019 American Mathematical Society. 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) ...
On critical values of polynomials with real critical points

Hinkkanen A.; Kayumov I. (2010)

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 ...
Smales problem for critical points on certain two rays

Hinkkanen A.; Kayumov I. (2010)

Let f be a polynomial of degree n ≥ 2 with f(0)= 0 and f′(0)= 1. We prove that there is a critical point ζ of f with |f(ζ)/ζ| ≤ 1/2 provided that the critical points of f lie in the sector {re iθ:r > 0,|θ| ≤ π/6}, and ...

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