scholarly journals Parametric Representations and Boundary Fixed Points of Univalent Self-Maps of the Unit Disk

2017 ◽  
pp. 67-85 ◽  
Author(s):  
Pavel Gumenyuk
Keyword(s):  
Fixed Points ◽  
Unit Disk ◽  
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 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.

scholarly journals Commuting finite Blaschke products with no fixed points in the unit disk

2009 ◽  
Vol 359 (2) ◽  
pp. 547-555 ◽  
Author(s):  
Manuela Basallote ◽  
Manuel D. Contreras ◽  
Carmen Hernández-Mancera
Keyword(s):  
Fixed Points ◽  
Unit Disk ◽  
Blaschke Products ◽  
Finite Blaschke Products
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