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

2017/03/16 by Pavel Gumenyuk, Gumenyuk, Pavel, Dmitri Prokhorov +1
Mathematics · #30C35 #30C55 #30C75 #30C80 (Secondary) #30D05 (Primary) #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1703.05835

openalex publication_date 2017/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Related

• Parametric representations and boundary fixed points of univalent self-maps of the unit disk
• Value Ranges of Univalent Self-Mappings of the Unit Disc
• Semigroup-fication of univalent self-maps of the unit disc
• Denjoy-Wolff points on the bidisk via models
• Boundary distortion estimates for holomorphic maps