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Schwarz-Pick Type Inequalities

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ISBN-10: 3764399996

ISBN-13: 9783764399993

Edition: 2009

Authors: Farit G. Avkhadiev, Karl-Joachim Wirths

List price: $69.99
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Description:

This book discusses in detail the extension of the Schwarz-Pick inequality to higher order derivatives of analytic functions with given images. It is the first systematic account of the main results in this area. Recent results in geometric function theory presented here include the attractive steps on coefficient problems from Bieberbach to de Branges, applications of some hyperbolic characteristics of domains via Beardon-Pommerenke's theorem, a new interpretation of coefficient estimates as certain properties of the Poincaré metric, and a successful combination of the classical ideas of Littlewood, Löwner and Teichmüller with modern approaches. The material is complemented with…    
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Book details

List price: $69.99
Copyright year: 2009
Publisher: Birkhauser Verlag GmbH
Publication date: 2/20/2009
Binding: Paperback
Pages: 156
Size: 6.75" wide x 9.50" long x 0.50" tall
Weight: 0.748
Language: English

Introduction
Historical remarks
On inequalities for higher derivatives
On methods
Survey of the contents
Basic coefficient inequalities
Subordinate functions
Bieberbach's conjecture by de Branges
Theorems of Jenkins and Sheil-Small
Inverse coefficients
Domains with bounded boundary rotation
The Poincar� metric
Background
The Schwarz-Pick inequality
Estimates using the Euclidean distance
An application of Teichm&uumlet;ller's theorem
Domains with uniformly perfect boundary
Derivatives of the conformal radius
Basic Schwarz-Pick type inequalities
Two classical inequalities
Theorems of Ruscheweyh and Yamashita
Pairs of simply connected domains
Holomorphic mappings into convex domains
Punishing factors for convex pairs
Case n=2 for all domains
Punishing factors for special cases
Solution of the Chua conjecture
Punishing factors for angles
Sharp lower bounds for punishing factors
Domains in the extended complex plane
Maps from convex into concave domains
Multiply connected domains
Finitely connected domains
Pairs of arbitrary domains
Some examples
Related results
Inequalities for schlicht functions
Derivatives of �-invariant functions
A characterization of convex domains
Some open problems
The Krzyz conjecture
The angle conjecture
The generalized Goodman conjecture
Bloch and several variable problems
On sums of inverse coefficients
Bibliography
Index