Sistema Bibliotecario de la Universidad de Quintana Roo

Basic coefficient inequalities -- The PoincarȨ metric -- Basic Schwarz-Pick type inequalities -- Punishing factors for special cases -- Multiply connected domains -- Related results -- Some open problems.

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 PoincarȨ metric, and a successful combination of the classical ideas of Littlewood, Lȵwner and Teichmȭller with modern approaches. The material is complemented with historical remarks on the Schwarz Lemma and a chapter introducing some challenging open problems. The book will be of interest for researchers and postgraduate students in function theory and hyperbolic geometry.

ZDB-2-SMA