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People’s Republic of China.


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 ?(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

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