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.

Keywords

• logharmonic mappings
• close to starlike
• positive real part
• radius of starlikeness and univalence.