An Extremal Problem for Odd Univalent Polynomials

Dmitrishin, Dmitriy; Gray, Daniel; Stokolos, Alexander; Tarasenko, Iryna; Дмитришин, Дмитро Володимирович; Тарасенко, Ірина

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dc.contributor.author	Dmitrishin, Dmitriy
dc.contributor.author	Gray, Daniel
dc.contributor.author	Stokolos, Alexander
dc.contributor.author	Tarasenko, Iryna
dc.contributor.author	Дмитришин, Дмитро Володимирович
dc.contributor.author	Тарасенко, Ірина	uk
dc.date.accessioned	2023-11-30T12:42:45Z
dc.date.available	2023-11-30T12:42:45Z
dc.date.issued	2023
dc.identifier.citation	An Extremal Problem for Odd Univalent Polynomials / D. Dmitrishin, D. Gray, A. Stokolos, I. Tarasenko // Computational Methods and Function Theory. - 2023. - P. 1-16.	en
dc.identifier.issn	1617-9447
dc.identifier.uri	10.1007/s40315-023-00487-3
dc.identifier.uri	http://dspace.opu.ua/jspui/handle/123456789/14181
dc.description.abstract	For the univalent polynomials F(z)=∑j=1Najz2j-1 with real coefficients and normalization a1= 1 we solve the extremal problem minaj:a1=1(-iF(i))=minaj:a1=1∑j=1N(-1)j+1aj. We show that the solution is 12sec2(π2N+2), and the extremal polynomial ∑j=1NU2(N-j+1)′(cos(π2N+2))U2N′(cos(π2N+2))z2j-1 is unique and univalent, where Uj(x) is a Chebyshev polynomial of the second kind and Uj′(x) denotes the derivative. As an application, we obtain an estimate of the Koebe radius for odd univalent polynomials in D and formulate several conjectures. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.	en
dc.language.iso	en_US	en
dc.publisher	Springer Science and Business Media Deutschland GmbH	en
dc.subject	Chebyshev polynomials	en
dc.subject	T-folded Koebe function	en
dc.subject	Koebe one-quarter theorem	en
dc.subject	Odd univalent polynomials	en
dc.title	An Extremal Problem for Odd Univalent Polynomials	en
dc.type	Article in Scopus	en
opu.citation.journal	Computational Methods and Function Theory	en
opu.citation.firstpage	1	en
opu.citation.lastpage	16	en
opu.staff.id	dmitrishin@op.edu.ua	en