Starlikeness associated with parabolic regions
A parabolic starlike function f of order ρ in the unit disk is characterized by the fact that the quantity zf′(z)/f(z) lies in a given parabolic region in the right half-plane. Denote the class of such functions by PS∗(ρ). This class is contained in the larger class of starlike functions of order ρ....
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.561 |
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| _version_ | 1832554411604312064 |
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| author | Rosihan M. Ali |
| author_facet | Rosihan M. Ali |
| author_sort | Rosihan M. Ali |
| collection | DOAJ |
| description | A parabolic starlike function f of order ρ in the unit disk is characterized by the fact that the quantity zf′(z)/f(z) lies in a given parabolic region in the right half-plane. Denote the class of such functions by PS∗(ρ). This class is contained in the larger class of starlike functions of order ρ. Subordination results for PS∗(ρ) are established, which yield sharp growth, covering, and distortion theorems. Sharp bounds for the first four coefficients are also obtained. There exist different extremal functions for these coefficient problems. Additionally, we obtain a sharp estimate for
the Fekete-Szegö coefficient functional and investigate convolution properties for PS∗(ρ). |
| format | Article |
| id | doaj-art-27f2064da0cd45e4a844c809432da160 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-27f2064da0cd45e4a844c809432da1602025-02-03T05:51:33ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005456157010.1155/IJMMS.2005.561Starlikeness associated with parabolic regionsRosihan M. Ali0School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, MalaysiaA parabolic starlike function f of order ρ in the unit disk is characterized by the fact that the quantity zf′(z)/f(z) lies in a given parabolic region in the right half-plane. Denote the class of such functions by PS∗(ρ). This class is contained in the larger class of starlike functions of order ρ. Subordination results for PS∗(ρ) are established, which yield sharp growth, covering, and distortion theorems. Sharp bounds for the first four coefficients are also obtained. There exist different extremal functions for these coefficient problems. Additionally, we obtain a sharp estimate for the Fekete-Szegö coefficient functional and investigate convolution properties for PS∗(ρ).http://dx.doi.org/10.1155/IJMMS.2005.561 |
| spellingShingle | Rosihan M. Ali Starlikeness associated with parabolic regions International Journal of Mathematics and Mathematical Sciences |
| title | Starlikeness associated with parabolic regions |
| title_full | Starlikeness associated with parabolic regions |
| title_fullStr | Starlikeness associated with parabolic regions |
| title_full_unstemmed | Starlikeness associated with parabolic regions |
| title_short | Starlikeness associated with parabolic regions |
| title_sort | starlikeness associated with parabolic regions |
| url | http://dx.doi.org/10.1155/IJMMS.2005.561 |
| work_keys_str_mv | AT rosihanmali starlikenessassociatedwithparabolicregions |