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Inequalities for the Angular Derivative of an Analytic Function in the Unit Disk
Author(s) -
Cowen Carl C.,
Pommerenke Christian
Publication year - 1982
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-26.2.271
Subject(s) - citation , library science , unit disk , mathematics , function (biology) , computer science , combinatorics , evolutionary biology , biology
Let $ be a function, analytic in the unit disk, D, that maps the unit disk into itself ((z) ^ 2). In this paper, we present some inequalities for the angular derivative of cj). The more important of these concern the derivative of $ at its fixed points in the closed unit disk. Since (f) and 0' need not be continuous in D we need to clarify the terms "fixed point" and "derivative of ^ at a fixed point".