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International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 1, Pages 189-192
http://dx.doi.org/10.1155/S0161171280000130

A covering theorem for odd typically-real functions

Department of Mathematical Sciences, University of Cincinnati, Cincinnati 45221, Ohio, USA

Received 20 July 1979

Copyright © 1980 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.

Abstract

An analytic function f(z)=z+a2z2+ in |z|<1 is typically-real if Imf(z)Imz0. The largest domain G in which each odd typically-real function is univalent (one-to-one) and the domain f(G) for all odd typically real functions f are obtained.