An Extremal Problem for Odd Univalent Polynomials

dc.contributor.author	Dmitrishin, D.
dc.contributor.author	Gray, D.
dc.contributor.author	Stokolos, A.
dc.contributor.author	Tarasenko, I.
dc.date.accessioned	2025-05-17T14:33:57Z
dc.date.available	2025-05-17T14:33:57Z
dc.date.issued	2024
dc.identifier.citation	Dmitrishin D. An Extremal Problem for Odd Univalent Polynomials / D. Dmitrishin, D. Gray, A. Stokolos, I. Tarasenko // Computational Methods and Function Theory, 24(1), 2024. - 83-100.	en
dc.identifier.uri	http://dspace.opu.ua/jspui/handle/123456789/15204
dc.description.abstract	For the univalent polynomials F(z) = P N j=1 aj z 2j−1 with real coefficients and normalization a1 = 1 we solve the extremal problem min aj : a1=1 (−iF(i)) = min aj : a1=1 X N j=1 (−1)j+1aj. We show that the solution is 1 2 sec2 π 2N+2 , and the extremal polynomial X N j=1 U ′ 2(N−j+1) cos π 2N+2 U ′ 2N cos π 2N+2 z 2j−1 is unique and univalent, where the Uj(x) are the Chebyshev polynomials of the second kind and U ′ j (x) denotes the derivative. As an application, we obtain the estimate of the Koebe radius for the odd univalent polynomials in D and formulate several conjectures.	en
dc.language.iso	en_US	en
dc.subject	Chebyshev polynomials	en
dc.subject	odd univalent polynomials	en
dc.subject	Koebe one-quarter theorem	en
dc.title	An Extremal Problem for Odd Univalent Polynomials	en
dc.type	Article	en
opu.citation.firstpage	83	en
opu.citation.lastpage	100	en