A sharp domain of univalence for the class of holomorphic self-mappings of a disc with inner and boundary fixed points

2021 ◽  
Vol 85 (5) ◽  
Author(s):  
Aleksei Petrovich Solodov
Keyword(s):  
Fixed Points ◽  
Boundary Fixed Points

scholarly journals Analytic flows on the unit disk: angular derivatives and boundary fixed points

2005 ◽  
Vol 222 (2) ◽  
pp. 253-286 ◽  
Author(s):  
Manuel D. Contreras ◽  
Santiago Díaz-Madrigal
Keyword(s):  
Fixed Points ◽  
Unit Disk ◽  
Angular Derivatives ◽  
Boundary Fixed Points

scholarly journals Infinitesimal generators of semigroups with prescribed boundary fixed points

2020 ◽  
Vol 10 (3) ◽  
Author(s):  
Manuel D. Contreras ◽  
Santiago Díaz-Madrigal ◽  
Pavel Gumenyuk
Keyword(s):  
Fixed Points ◽  
Infinitesimal Generators ◽  
Boundary Fixed Points

scholarly journals On boundary critical points for semigroups of analytic functions

2006 ◽  
Vol 98 (1) ◽  
pp. 125 ◽  
Author(s):  
M. D. Contreras ◽  
S. Díaz-Madrigal ◽  
Ch. Pommerenke
Keyword(s):  
Fixed Points ◽  
Unit Disk ◽  
Critical Points ◽  
Analytic Functions ◽  
Infinitesimal Generators ◽  
Contact Points ◽  
Angular Derivatives ◽  
Boundary Fixed Points ◽  
The Relationship ◽  
New Inequalities

We analyze the relationship between boundary fixed points of semigroups of analytic functions and boundary critical points of their infinitesimal generators. As a consequence, we show two new inequalities for analytic self-maps of the unit disk. The first one is about angular derivatives at fixed points of functions belonging to semigroups of analytic functions. The second one deals with angular derivatives at contact points of arbitrary analytic functions from the unit disk into itself.

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