Coefficient Bounds for Certain Analytic Functions
Let φ be an analytic function with the positive real parts, φ ( 0 ) = 1 and φ ′ ( 0 ) > 0 . Let f ( z ) = z + a 2 z 2 + a 3 z 3 + ⋯ be an analytic function satisfying the subordination α f ′ ( z ) + ( 1 - α ) z f ′ ( z ) / f ( z ) ≺ φ ( z ) , ( f ′ ( z ) ) α ( z f ′ ( z ) / f ( z ) ) ( 1 - α ) ≺...
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| Veröffentlicht in: | Bulletin of the Malaysian Mathematical Sciences Society 2018, Vol.41 (1), p.455-490 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
φ
be an analytic function with the positive real parts,
φ
(
0
)
=
1
and
φ
′
(
0
)
>
0
. Let
f
(
z
)
=
z
+
a
2
z
2
+
a
3
z
3
+
⋯
be an analytic function satisfying the subordination
α
f
′
(
z
)
+
(
1
-
α
)
z
f
′
(
z
)
/
f
(
z
)
≺
φ
(
z
)
,
(
f
′
(
z
)
)
α
(
z
f
′
(
z
)
/
f
(
z
)
)
(
1
-
α
)
≺
φ
(
z
)
,
(
f
′
(
z
)
)
α
(
1
+
z
f
″
(
z
)
/
f
′
(
z
)
)
(
1
-
α
)
≺
φ
(
z
)
,
(
f
(
z
)
/
z
)
α
(
z
f
′
(
z
)
/
f
(
z
)
)
(
1
-
α
)
≺
φ
(
z
)
, or
(
f
(
z
)
/
z
)
α
(
1
+
z
f
″
(
z
)
/
f
′
(
z
)
)
(
1
-
α
)
≺
φ
(
z
)
. For these functions, the bounds for the second Hankel determinant
a
2
a
4
-
a
3
2
as well as the Fekete–Szegö coefficient functional are obtained. Our results include some previously known results. |
|---|---|
| ISSN: | 0126-6705 2180-4206 |
| DOI: | 10.1007/s40840-016-0414-3 |