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

Abstract

In this paper we find the exact value region $\mathcal{V}(z_0,T)$ of the point evaluation functional $f\mapsto f(z_0)$ over the class of all holomorphic injective self-maps $f:\mathbb{D}\to \mathbb{D}$ of the unit disk $\mathbb{D}$ having a boundary regular fixed point at $\sigma =-1$ with $f^{\prime }(-1)=e^T$ and the Denjoy - Wolff point at $\tau =1$.

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

References in corpus (1)

• A Sharp Condition for the Loewner Equation to Generate Slits