Regions of Variability for Subclasses of Univalent Functions: Regions of Variability

The subject of univalent functions is an important area within the venerable field of complex analysis. In this subject one often considers subclasses of the class of all analytic and univalent functions defined on the unit disk in the complex plane that are normalized. A more challenging problem is to determine a region of variability for a given subclass. Region of variability problems typically give more exact information about a family of univalent functions than classical growth distortion and rotation theorems. This book deals with a number of region of variability problems defined on several subclasses of univalent functions. The region of variability and subclasses considered in this book are of current interest of other researchers. The growth estimate and the sharp Bloch semi-norm and the pre-Schwarzian norm are obtained in many cases. In addition, the pictorial illustrations concerning the region of variability using Mathematica make the reading of this book an enjoyable one. Some of the investigations presented in the book could lead to new results in different area of research in function theory.

Dr. Vasudeva Rao Allu has obtained his Ph.D. from IIT Madras, India in 2010. The author did his Post-Doctoral studies at Israel Institute of Technology. Currently he is a Post-Doctoral Fellow at the Department of Mathematics, IIT Madras, India. His current areas of interests are Univalent Function Theory and Harmonic Mappings.