Journal of Inequalities and Applications
Volume 6 (2001), Issue 6, Pages 651-664

Dynamics of inequalities in geometric function theory

Mark Elin,1 Simeon Reich,2 and David Shoikhet1

1Department of Applied Mathematics, ORT Braude College, Karmiel 21982, Israel
2Department of Mathematics, The Technion – Israel Institute of Technology, Haifa 32000, Israel

Received 4 April 2000; Revised 28 June 2000

Copyright © 2001 Mark Elin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A domain in the complex plane which is star-like with respect to a boundary point can be approximated by domains which are star-like with respect to interior points. This approximation process can be viewed dynamically as an evolution of the null points of the underlying holomorphic functions from the interior of the open unit disk towards a boundary point. We trace these dynamics analytically in terms of the Alexander–Nevanlinna and Robertson inequalities by using the framework of complex dynamical systems and hyperbolic monotonicity.