Second-order differential superordination for analytic functions in the upper half-plane
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Authors
Huo Tang
- School of Mathematics and Statistics, Chifeng University, Chifeng 024000, Inner Mongolia, People's Republic of China.
H. M. Srivastava
- Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada.
- Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China.
Guan-Tie Deng
- School of Mathematical Sciences, Beijing Normal University, Beijing 100875, People's Republic of China.
Shu-Hai Li
- School of Mathematics and Statistics, Chifeng University, Chifeng 024000, Inner Mongolia, People's Republic of China.
Abstract
Let \(\Omega\) be a set in the complex plane \(\mathbb{C}\). Also let \(p(z)\) be analytic in the upper half-plane \(\Delta=\{z:z\in\mathbb{C}\ \text{and}\ \Im(z)>0\}\) and suppose that \(\psi: \mathbb{C}^3\times\Delta\rightarrow\mathbb{C}\).
In this paper, we investigate the problem of determining properties of functions \(p(z)\) that satisfy the following second-order differential superordination:
\[\Omega\subset\left\{\psi\left(p(z),p'(z),p''(z);z\right): z\in\Delta\right\}.\]
Applications of these results to second-order differential superordination for analytic functions in \(\Delta\) are also presented.
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ISRP Style
Huo Tang, H. M. Srivastava, Guan-Tie Deng, Shu-Hai Li, Second-order differential superordination for analytic functions in the upper half-plane, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 10, 5271--5280
AMA Style
Tang Huo, Srivastava H. M., Deng Guan-Tie, Li Shu-Hai, Second-order differential superordination for analytic functions in the upper half-plane. J. Nonlinear Sci. Appl. (2017); 10(10):5271--5280
Chicago/Turabian Style
Tang, Huo, Srivastava, H. M., Deng, Guan-Tie, Li, Shu-Hai. "Second-order differential superordination for analytic functions in the upper half-plane." Journal of Nonlinear Sciences and Applications, 10, no. 10 (2017): 5271--5280
Keywords
- Differential subordination
- differential superordination
- analytic functions
- admissible functions
- upper half-plane
MSC
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