Third-Order Differential Subordination and Superordination Results for Meromorphically Multivalent Functions Associated with the Liu-Srivastava Operator
| dc.contributor.author | Tang, Huo | |
| dc.contributor.author | Srivastava, Hari M. | |
| dc.contributor.author | Li, Shu-Hai | |
| dc.contributor.author | Ma, Lin-Na | |
| dc.date.accessioned | 2017-11-05T14:10:27Z | |
| dc.date.available | 2017-11-05T14:10:27Z | |
| dc.date.copyright | 2014 | en_US |
| dc.date.issued | 2014 | |
| dc.description.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), ZP' (Z), Z^2P''(Z), Z^3P'''(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. | en_US |
| dc.description.reviewstatus | Reviewed | en_US |
| dc.description.scholarlevel | Faculty | en_US |
| dc.description.sponsorship | The research was partly supported by the Natural Science Foundation of China under Grant 11271045, the Higher School Doctoral Foundation of China under Grant 20100003110004, the Natural Science Foundation of Inner Mongolia of China under Grant 2010MS0117, and the Higher School Foundation of Inner Mongolia of China under Grant NJZY13298. The authors would like to thank Professors Om P. Ahuja and V. Ravichandran for their valuable suggestions and the referees for their careful reading and helpful comments to improve their paper. | en_US |
| dc.identifier.citation | Tang, H., Srivastava, H.M., Li, S., & Ma, L. (2014). Third-Order Differential Subordination and Superordination Results for Meromorphically Multivalent Functions Associated with the Liu-Srivastava Operator. Abstract and Applied Analysis, Vol. 2014, Article ID 792175. | en_US |
| dc.identifier.uri | http://dx.doi.org/10.1155/2014/792175 | |
| dc.identifier.uri | http://hdl.handle.net/1828/8778 | |
| dc.language.iso | en | en_US |
| dc.publisher | Abstract and Applied Analysis | en_US |
| dc.subject.department | Department of Mathematics and Statistics | |
| dc.title | Third-Order Differential Subordination and Superordination Results for Meromorphically Multivalent Functions Associated with the Liu-Srivastava Operator | en_US |
| dc.type | Article | en_US |