International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 1, Pages 189-192
doi: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 E. P. Merkes. 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)Imz≥0. 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.