International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 563-573
doi:10.1155/S0161171296000786
Close-to-starlike logharmonic mappings
Department of Mathematical Sciences, P O Box 223, KFUPM, Dhahran, Saudi Arabia
Received 22 February 1994; Revised 31 October 1994
Copyright © 1996 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|2βhg¯ defined on the unit disc U which can be written as the product of a logharmonic mapping with positive real part and a univalent starlike logharmonic mapping. Such mappings will be called close-to-starlike logharmonic mappings. Representation theorems and distortion theorems are obtained. Moreover, we determine the radius of univalence and starlikeness of these mappings.