On geometrical properties of logharmonic mappings

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 $% |z|\leq r$ 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.