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On Convex Functions with Complex Order Through Bounded Boundary Rotation
Let F be the class of functions f ( z ) = z + a 2 z 2 + ⋯ which are analytic in D = { z : | z | < 1 } and satisfies the condition 1 + 1 b z f ′ ′ ( z ) f ′ ( z ) = p t ( z ) , ( b ≠ 0 , b ∈ C , z ∈ D ) where p t ( z ) = t 4 + 1 2 p 1 ( z ) - t 4 - 1 2 p 2 ( z ) , t ≥ 2 , p 1 ( z ) , p 2 ( z ) ∈ P...
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| Published in: | Mathematics in computer science 2019-09, Vol.13 (3), p.433-439 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
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| Summary: | Let
F
be the class of functions
f
(
z
)
=
z
+
a
2
z
2
+
⋯
which are analytic in
D
=
{
z
:
|
z
|
<
1
}
and satisfies the condition
1
+
1
b
z
f
′
′
(
z
)
f
′
(
z
)
=
p
t
(
z
)
,
(
b
≠
0
,
b
∈
C
,
z
∈
D
)
where
p
t
(
z
)
=
t
4
+
1
2
p
1
(
z
)
-
t
4
-
1
2
p
2
(
z
)
,
t
≥
2
,
p
1
(
z
)
,
p
2
(
z
)
∈
P
.
P
is the class of analytic functions with the positive real part (Caratheodory class) then this function will be called convex function by means of bounded boundary rotation and denoted by
K
(
t
,
b
). In this present paper, we will introduce this class and its some properties. |
|---|---|
| ISSN: | 1661-8270 1661-8289 |
| DOI: | 10.1007/s11786-019-00405-8 |