This article is cited in 25 papers

Holomorphic mappings of the unit disc into itself with two fixed points

V. V. Goryainov

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

Abstract: The paper is concerned with holomorphic mappings of the unit disc into itself with two fixed points. Two cases are considered: when one fixed point lies inside the disc and the other lies on the boundary and when both fixed points lie on the boundary. The effect that angular derivatives at boundary fixed points have on the properties of functions inside the unit disc is studied. Conditions on the angular derivatives to guarantee the existence of domains of univalence inside the unit disc are given. The effect of the angular derivatives on the values of the Taylor coefficients of functions is also examined.
Bibliography: 19 titles.

Keywords: holomorphic mapping, fixed point, domain of univalence, angular derivative, coefficient region.

UDC: 517.54

MSC: Primary 30C55; Secondary 30C50, 30J99, 30C75

Received: 22.08.2016 and 17.10.2016

DOI: 10.4213/sm8802

 English version: Sbornik: Mathematics, 2017, 208:3, 360–376

Bibliographic databases:

• 
• 
• 
• 
• 
•