Treffer: On the boundary derivative for univalent functions
Title:
On the boundary derivative for univalent functions
Authors:
Source:
Mathematische Annalen. 276:499-504
Publisher Information:
Springer Science and Business Media LLC, 1987.
Publication Year:
1987
Subject Terms:
510.mathematics, Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems, starlike, General theory of univalent and multivalent functions of one complex variable, Quasiconformal mappings in the complex plane, 0101 mathematics, 01 natural sciences, Article
Document Type:
Fachzeitschrift
Article
File Description:
application/xml; image/jpeg; application/pdf
Language:
English
ISSN:
1432-1807
0025-5831
0025-5831
DOI:
10.1007/bf01450844
Access URL:
Rights:
Springer TDM
Accession Number:
edsair.doi.dedup.....1db0c1619f6b6d98cd0f539ad8d88f64
Database:
OpenAIRE
Weitere Informationen
Let f be analytic and univalent in the unit disc \({\mathbb{D}}\). The paper studies the relation between three notions of differentiability at a point \(\zeta\in \partial {\mathbb{D}}:\) (1) the angular derivative, (2) the unrestricted derivative, (3) the approximate derivative of the restriction of f to \(\partial {\mathbb{D}}\). It is shown that (1) and (3) are the same. If f(\({\mathbb{D}})\) is a quasidisc then the existence of (1) implies, for almost all \(\zeta\in \partial {\mathbb{D}}\), that of (2); this is not true in general if f(\({\mathbb{D}})\) is starlike.