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Applications of Livingston-type inequalities to the generalized Zalcman functional
Entity
UAM. Departamento de MatemáticasPublisher
Wiley-VCH VerlagDate
2018-04-02Citation
10.1002/mana.201700022
Mathematische Nachrichten 291.10 (2018): 1502-1513
ISSN
1522-2616 (online); 0025-584X (print)DOI
10.1002/mana.201700022Funded by
The authors are partially supported by MTM2015-65792-P from MINECO/FEDER-EU and the Thematic Research Network MTM2015-69323-REDT, MINECO, SpainProject
Gobierno de España. MTM2015-65792-P; Gobierno de España. MTM2015-69323-REDTEditor's Version
https://doi.org/10.1002/mana.201700022Subjects
30C45; 30C50; Hayman index; Hurwitz class; Noshiro–Warschawski class; Zalcman functional; Convex functions; Univalent functions; Starlike functions; MatemáticasNote
This is the peer-reviewed version of the following article: Efraimidis, I., & Vukotić, D. Applications of Livingston‐type inequalities to the generalized Zalcman functional. Mathematische Nachrichten 291.10 (2018): 1502-1513, which has been published in final form at https://doi.org/10.1002/mana.201700022. This article may be used for non-commercial purposes in accordance with Wiley-VCH Terms and Conditions for Self-ArchivingRights
© 2018 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimAbstract
We obtain sharp estimates for a generalized Zalcman coefficient functional with a complex parameter for the Hurwitz class and the Noshiro–Warschawski class of univalent functions as well as for the closed convex hulls of the convex and starlike functions by using an inequality from [6]. In particular, we generalize an inequality proved by Ma for starlike functions and answer a question from his paper [17]. Finally, we prove an asymptotic version of the generalized Zalcman conjecture for univalent functions and discuss various related or equivalent statements which may shed further light on the problem
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Google Scholar:Efraimidis, Iason
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Vukotic Jovsic, Dragan
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