Univalent Functions : A Primer

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 * An up-to-date resource on univalent functions * Covers introductory as well as research level material * Useful for graduate students and experienced researchers alike The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer Preface Contents List of Symbols 1. Univalent Functions – the Elementary Theory 2. Definitions of Major Subclasses 3. Fundamental Lemmas 4. Starlike and Convex Functions 5. Starlike and Convex Functions of Order α 6. Strongly Starlike and Convex Functions 7. Alpha-Convex Functions 8. Gamma-Starlike Functions 9. Close-to-Convex Functions 10. Bazilevič Functions 11. B 1 (α) Bazilevič Functions 12. The Class U(λ) 13. Convolutions 14. Meromorphic Univalent Functions 15. Loewner Theory 16. Other Topics 17. Open Problems Concluding Remarks Bibliography Index