International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 1, Pages 1-9
doi:10.1155/S0161171202111100
Typically real logharmonic mappings
Department of Computer Science, Mathematics and Statistics, American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates
Received 14 November 2001; Revised 24 January 2002
Copyright © 2002 Zayid Abdulhadi. 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
We consider logharmonic mappings of the form f(z)=z|z| 2βhg¯ defined on the unit disk U which are typically real. We obtain representation theorems and distortion theorems. We determine the radius of univalence and starlikeness of these mappings. Moreover, we derive a geometric characterization of such mappings.