English

Value regions of univalent self-maps with two boundary fixed points

Complex Variables 2017-03-29 v2

Abstract

In this paper we find the exact value region V(z0,T)\mathcal V(z_0,T) of the point evaluation functional ff(z0)f\mapsto f(z_0) over the class of all holomorphic injective self-maps f:DDf:\mathbb D\to\mathbb D of the unit disk D\mathbb D having a boundary regular fixed point at σ=1\sigma=-1 with f(1)=eTf'(-1)=e^{T} and the Denjoy - Wolff point at τ=1\tau=1.

Keywords

Cite

@article{arxiv.1703.05835,
  title  = {Value regions of univalent self-maps with two boundary fixed points},
  author = {Pavel Gumenyuk and Dmitri Prokhorov},
  journal= {arXiv preprint arXiv:1703.05835},
  year   = {2017}
}

Comments

In version 2, reference [13] and Figure 1 have been added