On the generalized Zalcman functional for some classes of univalent functions

2014/03/20 by Iason Efraimidis, Efraimidis, Iason, Dragan Vukotić +1
Mathematics · #30C45 #30C50 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30C45 #msc:30C50

paper · pdf · doi:10.48550/arxiv.1403.5240

arxiv created 2014/03/20 · arxiv updated 2014/03/21

Abstract

We prove three sharp estimates for the generalized Zalcman coefficient functional: one for the Hurwitz class, another for the Noshiro-Warschawski class, and yet another for the functions in the closed convex hull of convex univalent functions. In each case the extremal functions are identified. We also observe that an asymptotic version of the Zalcman conjecture is true.

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