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On Parabolic Analytic Functions with Respect to Symmetrical Points |
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PP: 333-341 |
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doi:10.18576/amis/100135
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Author(s) |
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Khalida Inayat Noor,
Humayoun Shahid,
Muhammad Aslam Noor,
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Abstract |
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| Let A be the class of functions f , f (z) = z+
ех
m=2
amzm, analytic in the open unit disc E. Let S∗
s (h) consist of functions
f ∈ A such that 2z f ′(z)
f (z)−f (−z) ≺ h(z), where ≺ denotes subordination and h(z) is analytic in E with h(0) = 1. For n = 0,1,2,3, . . . , a
certain integral operator In : A→A is defined as In f = f−1
n ∗ f such that ( f−1
n ∗ fn)(z) = z
z−1 , where fn(z) = z
(1−z)n+1 , and ∗ denotes
convolution. By taking h(z) =1+ 2
p2 log 1+
√
z
1−
√
z 2a
,0
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