English

On the generalized Zalcman functional for some classes of univalent functions

Complex Variables 2014-03-21 v1

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.

Keywords

Cite

@article{arxiv.1403.5240,
  title  = {On the generalized Zalcman functional for some classes of univalent functions},
  author = {Iason Efraimidis and Dragan Vukotić},
  journal= {arXiv preprint arXiv:1403.5240},
  year   = {2014}
}