上半平面中解析函数的微分从属和微分超从属

数学物理学报 ›› 2016, Vol. 36 ›› Issue (2): 201-214.

• 论文 • 下一篇

上半平面中解析函数的微分从属和微分超从属

汤获^1,2, Srivastava H M³, 邓冠铁²

1. 赤峰学院数学与统计学院内蒙古赤峰 024000;
2. 北京师范大学数学科学学院北京 100875;
3. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada

收稿日期:2015-11-03 修回日期:2016-02-08 出版日期:2016-04-25 发布日期:2016-04-25
作者简介:汤获,thth2009@163.com;Srivastava H M,harimsri@math.uvic.ca;邓冠铁,denggt@bnu.edu.cn
基金资助:
国家自然科学基金(11561001,11271045);内蒙古自然科学基金(2010MS0117,2014MS0101)和内蒙古高等学校科研基金(NJZY240,NJZY13298)资助

Differential Subordination and Differential Superordination for Analytic Functions in the Upper Half-Plane

Tang Huo^1,2, Srivastava H³, Deng Guantie²

1 School of Mathematics and Statistics, Chifeng University, Inner Mongolia Chifeng 024000;
2 School of Mathematical Sciences, Beijing Normal University, Beijin 100875;
3 Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada

Received:2015-11-03 Revised:2016-02-08 Online:2016-04-25 Published:2016-04-25
Supported by:
Supported by the NSFC (11561001, 11271045), the Natural Science Foundation of Inner Mongolia (2010MS0117, 2014MS0101) and the Higher School Foundation of Inner Mongolia (NJZY240, NJZY13298)

摘要/Abstract

摘要：

设Ω为复平面C上的任意子集,函数p在上半平面Δ={z:z∈C和Im(z)>0}内解析,且设ψ:C³×Δ→C.该文建立了上半平面Δ内满足下列二阶微分超从属条件Ω⊂{ψ(p(z),p'(z),p"(z);z):z∈Δ}的函数p的基本理论.作为该理论的应用,该文还得到了Δ内解析函数的某些微分从属和微分超从属结果.

关键词: 微分从属, 微分超从属, 解析函数, 允许函数, 上半平面

Abstract:

Let Ω be a set in the complex plane C. Also let p be analytic in the upper half-plane Δ={z:z∈C and Im(z)>0} and suppose that ψ: C³×Δ→C. In this paper, we consider the problem of determining properties of functions p that satisfy the following differential superordination Ω⊂{ψ(p(z), p'(z), p"(z);z): z∈Δ}. Applications of these results to differential subordination and differential superordination for analytic functions in Δ are also presented.

Key words: Differential subordination, Differential superordination, Analytic functions, Admissible functions, Upper half-plane

中图分类号:

O174.5

汤获, Srivastava H M, 邓冠铁. 上半平面中解析函数的微分从属和微分超从属[J]. 数学物理学报, 2016, 36(2): 201-214.

Tang Huo, Srivastava H, Deng Guantie. Differential Subordination and Differential Superordination for Analytic Functions in the Upper Half-Plane[J]. Acta mathematica scientia,Series A, 2016, 36(2): 201-214.

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上半平面中解析函数的微分从属和微分超从属

Differential Subordination and Differential Superordination for Analytic Functions in the Upper Half-Plane

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