Univalent polynomials and Koebe’s one-quarter theorem

dc.contributor.author	Dmitrishin, Dmitriy
dc.contributor.author	Dyakonov, Konstantin
dc.contributor.author	Stokolos, Alex
dc.date.accessioned	2025-01-22T13:28:38Z
dc.date.available	2025-01-22T13:28:38Z
dc.date.issued	2019
dc.identifier.citation	Dmitrishin D. Univalent polynomials and Koebe’s one-quarter theorem / D. Dmitrishin, K. Dyakonov, A. Stokolos // Analysis and Mathematical Physics, 2019	en
dc.identifier.uri	http://dspace.opu.ua/jspui/handle/123456789/14853
dc.description.abstract	The famous Koebe 1 4 theorem deals with univalent (i.e., injective) analytic functions f on the unit disk D. It states that if f is normalized so that f(0) = 0 and f ′ (0) = 1, then the image f(D) contains the disk of radius 1 4 about the origin, the value 1 4 being best possible. Now suppose f is only allowed to range over the univalent polynomials of some fixed degree. What is the optimal radius in the Koebe-type theorem that arises? And for which polynomials is it attained? A plausible conjecture is stated, and the case of small degrees is settled.	en
dc.language.iso	en	en
dc.title	Univalent polynomials and Koebe’s one-quarter theorem	en
dc.type	Article	en
opu.citation.journal	Analysis and Mathematical Physics	en
opu.citation.issue	2019	en