Schwarz-Pick Type Inequalities

  • Farit G. Avkhadiev
  • Karl-Joachim Wirths

Part of the Frontiers in Mathematics book series (FM)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Pages 1-6
  3. Pages 27-48
  4. Pages 113-126
  5. Pages 127-142
  6. Back Matter
    Pages 143-156

About this book


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 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.


Area Factor Lemma Schwarz lemma analytic function boundary element method character derivative function functional analysis functions geometry hyperbolic geometry inequalities theorem

Authors and affiliations

  • Farit G. Avkhadiev
    • 1
  • Karl-Joachim Wirths
    • 2
  1. 1.Chebotarev Research InstituteKazan State UniversityKazanRussia
  2. 2.Institut für Analysis und AlgebraTU BraunschweigBraunschweigGermany

Bibliographic information