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...
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| Sprache: | eng |
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| Zusammenfassung: | 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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| DOI: | 10.48550/arxiv.1610.01087 |