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Some Families of Analytic Functions in the Upper Half- Plane and Their Associated Differential Subordination and Differential Superordination Properties and Problems |
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PP: 1247-1257 |
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doi:10.18576/amis/110502
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Author(s) |
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Huo Tang,
H. M. Srivastava,
Guan-Tie Deng,
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Abstract |
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| The existing literature in Geometric Function Theory of Complex Analysis contains a considerably large number of
interesting investigations dealing with differential subordination and differential superordination problems for analytic functions in
the unit disk. Nevertheless, only a few of these earlier investigations deal with the above-mentioned problems in the upper half-plane.
The notion of differential subordination in the upper half-plane was introduced by R˘aducanu and Pascu in [16]. For a set W in the
complex plane C, let the function p(z) be analytic in the upper half-plane D given by
D = {z : z ∈ C and Á(z) > 0}
and suppose that y : C3×D →C. The main object of this article is to consider the problem of determining properties of functions p(z)
that satisfy the following differential superordination:
W ⊂
y
p(z), p′(z), p′′(z); z
: z ∈ D
.
We also present several applications of the results derived in this article to differential subordination and differential superordination
for analytic functions in D . |
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