伯努利双纽线区域内复阶解析函数类的优化问题

数学物理学报 ›› 2019, Vol. 39 ›› Issue (1): 156-164.

伯努利双纽线区域内复阶解析函数类的优化问题

汤获*(),李书海(),牛潇萌(),马丽娜()

赤峰学院数学与统计学院内蒙古赤峰 024000

收稿日期:2018-02-01 出版日期:2019-02-26 发布日期:2019-03-12
通讯作者: 汤获 E-mail:thth2009@163.com;lishms66@163.com;ndnxm@126.com;malina00@163.com
作者简介:李书海, E-mail:lishms66@163.com|牛潇萌, E-mail:ndnxm@126.com|马丽娜, E-mail:malina00@163.com
基金资助:
国家自然科学基金(11561001);国家自然科学基金(11271045);内蒙古高校青年科技英才支持计划项目(NJYT-18-A14);内蒙古自然科学基金(2018MS01026);内蒙古自然科学基金(2014MS0101);内蒙古自然科学基金(2017MS0113);内蒙古高校科研基金(NJZY17300);内蒙古高校科研基金(NJZY18217);赤峰市自然科学研究课题

Majorization Problems for the Classes of Analytic Functions of Complex Order on the Domains of Lemniscate of Bernoulli

Huo Tang*(),Shuhai Li(),Xiaomeng Niu(),Lina Ma()

School of Mathematics and Statistics, Chifeng University, Inner Mongolia Chifeng 024000

Received:2018-02-01 Online:2019-02-26 Published:2019-03-12
Contact: Huo Tang E-mail:thth2009@163.com;lishms66@163.com;ndnxm@126.com;malina00@163.com
Supported by:
the NSFC(11561001);the NSFC(11271045);the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(NJYT-18-A14);the Natural Science Foundation of Inner Mongolia(2018MS01026);the Natural Science Foundation of Inner Mongolia(2014MS0101);the Natural Science Foundation of Inner Mongolia(2017MS0113);the Higher School Foundation of Inner Mongolia(NJZY17300);the Higher School Foundation of Inner Mongolia(NJZY18217);the Natural Science Foundation of Chifeng

摘要/Abstract

摘要：

该文利用Salagean算子和从属关系分别引入了伯努利双纽线左、右半有界区域内复阶解析函数类L_n^γ和R_n^b（a，c），研究了该函数类的优化问题，并得到了一些有趣的推论.

关键词: 解析函数, 伯努利双纽线, Salagean算子, 从属关系, 优化

Abstract:

In this paper, we introduce the classes L_n^γ and R_n^b(a, c) of analytic functions on the left-half and right-half bounded domains of lemniscate of Bernoulli, which are defined by using the Salagean operator and subordination relationship, and investigate majorization problems for functions belonging to these classes. Some interesting corollaries of our main results are also considered.

Key words: Analytic function, Lemniscate of Bernoulli, Salagean operator, Subordination relationship, Majorization

中图分类号:

O174.5

汤获,李书海,牛潇萌,马丽娜. 伯努利双纽线区域内复阶解析函数类的优化问题[J]. 数学物理学报, 2019, 39(1): 156-164.

Huo Tang,Shuhai Li,Xiaomeng Niu,Lina Ma. Majorization Problems for the Classes of Analytic Functions of Complex Order on the Domains of Lemniscate of Bernoulli[J]. Acta mathematica scientia,Series A, 2019, 39(1): 156-164.

图/表 4

参考文献 19

1	MacGregor T H . Majorization by univalent functions. Duke Math J, 1967, 34: 95- 102 doi: 10.1215/S0012-7094-67-03411-4
2	Roberston M S . Quasi-subordination and coefficient conjectures. Bull Amer Math Soc, 1970, 76: 1- 9 doi: 10.1090/S0002-9904-1970-12356-4
3	Srivastava H M , Owa S . Current Topics in Analytic Function Theory. Singapore: World Scientific Publishing Company, 1992
4	Salagean G S . Subclasses of Univalent Functions. New York: Springer-Verlag, 1983
5	Mendiratta R , Nagpal S , Ravichandran V . A subclass of starlike functions associated with left-half of the lemniscate of Bernoulli. Int J Math, 2014, 25 (9): 1- 17
6	Sokol J . On some subclass of strongly starlike functions. Demonstratio Math, 1998, 21: 81- 86
7	Sokol J , Stankiewicz J . Radius of convexity of some subclasses of strongly starlike functions. Zesz Nauk Politech Rzeszowskiej Mat, 1996, 19: 101- 105
8	Altintas O , Srivastava H M . Some majorization problems associated with p-valently starlike and convex functions of complex order. East Asian Math J, 2001, 17 (2): 207- 218
9	Altintas O , Ozkan O , Srivastava H M . Majorization by starlike functions of complex order. Complex Var, 2001, 46: 207- 218
10	Goyal S , Goswami P . Majorization for certain classes of analytic functions defined by fractional derivatives. Appl Math Lett, 2009, 22 (12): 1855- 1858 doi: 10.1016/j.aml.2009.07.009
11	Goyal S P , Goswami P . Majorization for certain classes of meromorphic functions defined by integral operator. Ann Univ Mariae Curie Sklodowska Lublin-Polonia, 2012, 2: 57- 62
12	Goswami P , Aouf M K . Majorization properties for certain classes of analytic functions using the Salagean operator. Appl Math Lett, 2010, 23 (11): 1351- 1354 doi: 10.1016/j.aml.2010.06.030
13	Prajapat J K , Aouf M K . Majorization problem for certain class of p-valently analytic functions defined by generalized fractional differintegral operator. Comput Math Appl, 2012, 63: 42- 47 doi: 10.1016/j.camwa.2011.10.065
14	Tang Huo , Deng Guantie , Li Shuhai . Majorization properties for certain classes of analytic functions involving a generalized differential operator. J Math Res Appl, 2013, 33 (5): 578- 586
15	Tang Huo , Li Shuhai , Deng Guantie . Majorization properties for a new subclass of θ-spiral functions of order γ. Math Slovaca, 2014, 64 (1): 39- 50
16	Li Shuhai , Tang Huo , Ao En . Majorization properties for certain new classes of analytic functions using the Salagean operator. J Inequal Appl, 2013, 2013: 86 doi: 10.1186/1029-242X-2013-86
17	Tang Huo , Aouf M K , Deng Guantie . Majorization problems for certain subclasses of meromorphic multivalent functions associated with the Liu-Srivastava operator. Filomat, 2015, 29 (4): 763- 772 doi: 10.2298/FIL1504763T
18	Goodman A W . Univalent Functions. Tampa: Mariner Publishing Company, 1983
19	Nehari Z . Conformal Mapping. New York: MacGraw-Hill Book Company, 1955

[1]	胡玲莉, 方东辉. 带锥约束的复合优化问题的最优性条件[J]. 数学物理学报, 2018, 38(6): 1112-1121.
[2]	李润鑫,黄辉,尚振宏,曹宇,王红斌,张晶. 多目标约束向量优化问题的类拉格朗日乘数法[J]. 数学物理学报, 2018, 38(6): 1076-1094.
[3]	李向利,师娟娟,董晓亮. 一类修正的非单调谱共轭梯度法及其在非负矩阵分解中的应用[J]. 数学物理学报, 2018, 38(5): 954-962.
[4]	方东辉,刘伟玲. 带复合函数的分式优化问题的Farkas引理[J]. 数学物理学报, 2018, 38(5): 842-854.
[5]	马丽娜, 李书海, 牛潇萌, 张海燕. 关于对称共轭点的倒星象函数某些子类的系数估计[J]. 数学物理学报, 2018, 38(1): 10-23.
[6]	孙祥凯. 不确定信息下凸优化问题的鲁棒解刻划[J]. 数学物理学报, 2017, 37(2): 257-264.
[7]	玄祖兴, 徐洪焱. 解析函数的Borel方向与唯一性[J]. 数学物理学报, 2016, 36(4): 740-749.
[8]	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.
[9]	李英毅, 张海斌, 高欢. 一类修正邻近梯度法及其收敛性[J]. 数学物理学报, 2015, 35(6): 1136-1145.
[10]	李书海, 汤获, 马丽娜, 敖恩. 与条形区域有关的解析函数新子类[J]. 数学物理学报, 2015, 35(5): 970-986.
[11]	王月虎, 张从军. 广义均衡问题的算法及强收敛性——基于Wiener-Hopf方程技巧[J]. 数学物理学报, 2015, 35(4): 695-709.
[12]	柴艳飞, 刘三阳, 李军. 集值优化问题严格有效解的一、二阶最优性条件[J]. 数学物理学报, 2014, 34(1): 193-206.
[13]	周树清, 胡振华, 彭冬云. 一类A -调和方程的障碍问题的很弱解的全局正则性[J]. 数学物理学报, 2014, 34(1): 27-38.
[14]	熊良鹏, 刘晓丽. 从属解析函数族的有限阶哈达玛乘积[J]. 数学物理学报, 2014, 34(1): 150-156.
[15]	徐洪焱, 易才凤, 胡祎. Laplace-Stieltjes变换所表示的解析函数的对数级与对数精确级[J]. 数学物理学报, 2013, 33(2): 366-376.