Abstract
In this paper we investigate some applications of the differential subordination and superordination of classes of admissible functions associated with an integral operator. Additionally, differential sandwich-type results are obtained.
Highlights
Let H(U) be the class of functions analytic in the disk U = {z ∈ C : |z| < 1} and H[a, n] be the subclass of H (U) consisting of functions of the form:f (z) = a + anzn + an+1zn+1 + . . . .Let f and F be members of H(U), the function f (z) is said to be subordinate to F (z), or F (z) is said to be superordinate to f (z), if there exists a function ω(z) analytic in U with ω(0) = 0 and |ω(z)| < 1, z ∈ U, such that f (z) = F (ω(z))
Aouf and Seoudy [6] investigated a subordination and superordination problems for multivalent functions defined by the integral operator Ipα, they have determined classes of admissible functions so that q1(z) ≺ Ipαf (z) ≺ q2(z) and q1(z)
The dual problem of differential subordination, that is, differential superordination of the integral operator Ipα is investigated. For this purpose the class of admissible functions is given in the following definition
Summary
Admissible classes of multivalent functions associated with an integral operator Abstract. In this paper we investigate some applications of the differential subordination and superordination of classes of admissible functions associated with an integral operator.
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