The study of univalent functions dates back to the early years of the 20th century, and is one of the most popular research areas in complex analysis. This book is directed at introducing and bringing up to date current research in the area of univalent functions, with an emphasis on the important subclasses, thus providing an accessible resource suitable for both beginning and experienced researchers.



Contents
Univalent Functions – the Elementary Theory
Definitions of Major Subclasses
Fundamental Lemmas
Starlike and Convex Functions
Starlike and Convex Functions of Order α
Strongly Starlike and Convex Functions
Alpha-Convex Functions
Gamma-Starlike Functions
Close-to-Convex Functions
Bazilevič Functions
B1(α) Bazilevič Functions
The Class U(λ)
Convolutions
Meromorphic Univalent Functions
Loewner Theory
Other Topics
Open Problems