Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2014, Special Issue (2014), Article ID 792175, 11 pages.
Third-Order Differential Subordination and Superordination Results for Meromorphically Multivalent Functions Associated with the Liu-Srivastava Operator
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 . Also let be analytic in the unit disk and suppose that . In this paper, we investigate the problem of determining properties of functions that satisfy the following third-order differential superordination: . 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.
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 792175, 11 pages.
First available in Project Euclid: 6 October 2014
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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