Multivalent and in particular univalent functions play an important
role in complex analysis. Great interest was aroused when de
Branges in 1985 settled the long-standing Bieberbach conjecture for
the coefficients of univalent functions. The second edition of
Professor Hayman's celebrated book is the first to include a full
and self-contained proof of this result, with a new chapter devoted
to it. Another new chapter deals with coefficient differences of
mean p-valent functions. The book has been updated in several other
ways, with recent theorems of Baernstein and Pommerenke on
univalent functions of restricted growth and Eke's regularity
theorems for the behaviour of the modulus and coefficients of mean
p-valent functions. Some of the original proofs have been
simplified. Each chapter contains examples and exercises of varying
degrees of difficulty designed both to test understanding and to
illustrate the material. Consequently the book will be useful for
graduate students and essential for specialists in complex function
theory.
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