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 a

Strongly Starlike and Convex Functions

Alpha-Convex Functions

Gamma-Starlike Functions

Close-to-Convex Functions

Bazilevic Functions

B1(a) Bazilevic Functions

The Class U(?)

Convolutions

Meromorphic Univalent Functions

Loewner Theory

Other Topics

Open Problems