Schwarz-Pick Type Inequalities
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 func
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Advisory Editorial Board Leonid Bunimovich (Georgia Institute of Technology, Atlanta) Benoît Perthame (Université Pierre et Marie Curie, Paris) Laurent Saloff-Coste (Cornell University, Ithaca) Igor Shparlinski (Macquarie University, New South Wales) Wolfgang Sprössig (TU Bergakademie Freiberg) Cédric Vilani (Ecole Normale Supérieure, Lyon)
Farit G. Avkhadiev Karl-Joachim Wirths
Schwarz-Pick Type
Inequalities
Birkhäuser Verlag Basel . Boston . Berlin
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Dedicated to our families
Contents 1
2
Introduction 1.1 Historical remarks . . . . . . . . . . 1.2 On inequalities for higher derivatives 1.3 On methods . . . . . . . . . . . . . . 1.4 Survey of the contents . . . . . . . .
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Basic coefficient inequalities 2.1 Subordinate functions . . . . . . . . . . . 2.2 Bieberbach’s conjecture by de Branges . . 2.3 Theorems of Jenkins and Sheil-Small . . . 2.4 Inverse coefficients . . . . . . . . . . . . . 2.5 Domains with bounded boundary rotation
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27 27 30 33 37 40 44
Basic Schwarz-Pick type inequalities 4.1 Two classical inequalities . . . . . . . . . . 4.2 Theorems of Ruscheweyh and Yamashita . 4.3 Pairs of simply c
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