International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 563-573
doi:10.1155/S0161171296000786

Close-to-starlike logharmonic mappings

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.