Abstract and Applied Analysis

Third-Order Differential Subordination and Superordination Results for Meromorphically Multivalent Functions Associated with the Liu-Srivastava Operator

Huo Tang, H. M. Srivastava, Shu-Hai Li, and Li-Na Ma

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 792175, 11 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412605986

Digital Object Identifier
doi:10.1155/2014/792175

Mathematical Reviews number (MathSciNet)
MR3232865

Zentralblatt MATH identifier
07023078

Citation

Tang, Huo; Srivastava, H. M.; Li, Shu-Hai; Ma, Li-Na. Third-Order Differential Subordination and Superordination Results for Meromorphically Multivalent Functions Associated with the Liu-Srivastava Operator. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 792175, 11 pages. doi:10.1155/2014/792175. https://projecteuclid.org/euclid.aaa/1412605986


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