International Journal of Mathematics and Mathematical Sciences 
Volume 31 (2002), Issue 1, Pages 1-9
doi:10.1155/S0161171202111100

Typically real logharmonic mappings

Zayid Abdulhadi

 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

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.