Bounds for the second Hankel determinant of certain univalent functions
The estimates for the second Hankel determinant a 2 a 4 − a 3 2 of the analytic function f ( z ) = z + a 2 z 2 + a 3 z 3 + ⋯ , for which either z f ′ ( z ) / f ( z ) or 1 + z f ″ ( z ) / f ′ ( z ) is subordinate to a certain analytic function, are investigated. The estimates for the Hankel determin...
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| Veröffentlicht in: | Journal of inequalities and applications 2013-06, Vol.2013 (1), Article 281 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | The estimates for the second Hankel determinant
a
2
a
4
−
a
3
2
of the analytic function
f
(
z
)
=
z
+
a
2
z
2
+
a
3
z
3
+
⋯
, for which either
z
f
′
(
z
)
/
f
(
z
)
or
1
+
z
f
″
(
z
)
/
f
′
(
z
)
is subordinate to a certain analytic function, are investigated. The estimates for the Hankel determinant for two other classes are also obtained. In particular, the estimates for the Hankel determinant of strongly starlike, parabolic starlike and lemniscate starlike functions are obtained.
MSC:
30C45, 30C80. |
|---|---|
| ISSN: | 1029-242X 1029-242X |
| DOI: | 10.1186/1029-242X-2013-281 |