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 t...
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| Veröffentlicht in: | arXiv.org 2016-10 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
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| Online-Zugang: | Volltext |
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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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| ISSN: | 2331-8422 |