伯努利双纽线区域内复阶解析函数类的优化问题

Abstract

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

CLC Number:

O174.5

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.

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References 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

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

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