On geometrical properties of logharmonic mappings

Abstract

In this paper, we find the radius of the disk ${\Omega }_r$ such that every starlike logharmonic mapping $f(z)$ of order $\alpha ,$ is starlike in with respect to any point of ${\Omega }_r.$ We also establish a relation between the set of starlike logharmonic mappings \ and the set of starlike logharmonic mappings of order alpha. Moreover, the radius of starlikeness and univalence for the set of close to starlike logharmonic mappings of order $\alpha$ is determined.