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arXiv · 1610.01087

On geometrical properties of logharmonic mappings

Zayid Abdulhadi·Layan El Hajj
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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 $% |z|\leq r$ 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.

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Zayid Abdulhadi, Layan El Hajj. 2016-10-04. On geometrical properties of logharmonic mappings. https://arxiv.org/abs/1610.01087

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