Schwarz-Pick Type Inequalities

Name: Schwarz-Pick Type Inequalities
Price: 45.5 USD
Availability: InStock
ISBN: 9783764399993

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 PoincarÃ© metric, and a successful combination of the classical ideas of Littlewood, LÃ¶wner and TeichmÃ¼ller with modern approaches. The material is complemented with…

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 Poincarï¿½ 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 ï¿½-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