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International Journal of Mathematics and Mathematical Sciences
Volume 2, Issue 2, Pages 163-186

An invitation on the study of univalent and multivalent functions

Department of Mathematics, University of South Florida, Tampa 33620, Florida, USA

Copyright © 1979 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We begin with the basic definition and some very simple examples from the theory of univalent functions. After a brief look at the literature, we survey the progress that has been made on certain problems in this field. The article ends with a few open questions.