In:
Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-11
Abstract:
There are many articles in the literature dealing with the first-order and the second-order differential subordination and superordination problems for analytic functions in the unit disk, but only a few articles are dealing with the above problems in the third-order case (see, e.g., Antonino and Miller (2011) and Ponnusamy et al. (1992)). The concept of the third-order differential subordination in the unit disk was introduced by Antonino and Miller in (2011). Let Ω be a set in the complex plane C . Also let p be analytic in the unit disk U = z : z ∈ C and z 〈 1 and suppose that ψ : C 4 × U → C . In this paper, we investigate the problem of determining properties of functions p ( z ) that satisfy the following third-order differential superordination: Ω ⊂ ψ p z , z p ′ z , z 2 p ′ ′ z , z 3 p ′ ′ ′ z ; z : z ∈ U . As applications, we derive some third-order differential subordination and superordination results for meromorphically multivalent functions, which are defined by a family of convolution operators involving the Liu-Srivastava operator. The results are obtained by considering suitable classes of admissible functions.
Type of Medium:
Online Resource
ISSN:
1085-3375
,
1687-0409
Language:
English
Publisher:
Hindawi Limited
Publication Date:
2014
detail.hit.zdb_id:
2064801-7
SSG:
17,1
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