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arXiv · 1611.00682

Applications of Livingston-type inequalities to the generalized Zalcman functional

Iason Efraimidis·Dragan Vukotić
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Abstract

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 [16]. 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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Iason Efraimidis, Dragan Vukotić. 2017-01-17. Applications of Livingston-type inequalities to the generalized Zalcman functional. https://doi.org/10.1002/mana.201700022

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