Some Families of Analytic Functions in the Upper Half- Plane and Their Associated Differential Subordination and Differential Superordination Properties and Problems

Authors

Huo Tang, School of Mathematics and Statistics, Chifeng University, Chifeng 024000, Inner Mongolia, People’s Republic of China.Follow
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.Follow
Guan-Tie Deng, School of Mathematical Sciences, Beijing Normal University, Beijing 100875, People’s Republic of China.Follow

Author Country (or Countries)

Republic of China.

Abstract

The existing literature in Geometric Function Theory of Complex Analysis contains a considerably large number of interesting investigations dealing with differential subordination and differential superordination problems for analytic functions in the unit disk. Nevertheless, only a few of these earlier investigations deal with the above-mentioned problems in the upper half-plane. The notion of differential subordination in the upper half-plane was introduced by R˘aducanu and Pascu in [16]. For a set W in the complex plane C, let the function p(z) be analytic in the upper half-plane D given by D = {z : z ∈ C and ?(z) > 0} and suppose that y : C3×D →C. The main object of this article is to consider the problem of determining properties of functions p(z) that satisfy the following differential superordination: W ⊂ y 􀀀 p(z), p′(z), p′′(z); z : z ∈ D. We also present several applications of the results derived in this article to differential subordination and differential superordination for analytic functions in D

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/110502

Recommended Citation

Tang, Huo; M. Srivastava, H.; and Deng, Guan-Tie (2017) "Some Families of Analytic Functions in the Upper Half- Plane and Their Associated Differential Subordination and Differential Superordination Properties and Problems," Applied Mathematics & Information Sciences: Vol. 11: Iss. 5, Article 2.
DOI: http://dx.doi.org/10.18576/amis/110502
Available at: https://digitalcommons.aaru.edu.jo/amis/vol11/iss5/2