GROWTH AND DISTORTION THEOREMS FOR ALMOST STARLIKE MAPPINGS OF COMPLEX ORDER λ

doi:10.1016/S0252-9602(18)30782-3

Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (3): 769-777.doi: 10.1016/S0252-9602(18)30782-3

• Articles • Previous Articles Next Articles

GROWTH AND DISTORTION THEOREMS FOR ALMOST STARLIKE MAPPINGS OF COMPLEX ORDER λ

Xiaofei ZHANG¹, Jin LU², Xiaofei LI¹

1. School of Mathematics and Statistics, Pingdingshan University, Pingdingshan 467000, China;
2. Department of Mathematics, Huzhou University, Zhejiang 313000, China

Received:2016-12-14 Revised:2017-08-22 Online:2018-06-25 Published:2018-06-25
Contact: Jin LU E-mail:luking@zjhu.edu.cn
Supported by:
Supported by the National Natural Science Foundation of China (11501198, 11701307), the Key Scientific Research Projects in Universities of Henan Province (16B110010), the Zhejiang Natural Science Foundation of China (LY16A010012), the Doctoral Foundation of Pingdingshan University (PXY-BSQD-2015005), and the Foster Foundation of Pingdingshan University (PXYPYJJ2016007).

Abstract

Xiaofei ZHANG, Jin LU, Xiaofei LI. GROWTH AND DISTORTION THEOREMS FOR ALMOST STARLIKE MAPPINGS OF COMPLEX ORDER λ[J].Acta mathematica scientia,Series B, 2018, 38(3): 769-777.

Trendmd

[1] Pommerenke C. Univalent Functions. Göttingen:Vandenhoeck Ruprecht, 1975
[2] Cartan H. Sur la possibilité d'étendre aux fonctions de plusieurs variables complex, La théorie des fonctions univalents//Paul Montel. Lecons sur les Fonctions Univalents ou Multivalentes. Pairs:GauthierVillars, 1933:125-155
[3] Barnard R W, Fitzgerald C H, Gong S. The growth and 1/4 theorems for starlike mappings in Cⁿ. Pac J Math, 1991, 150:13-22
[4] Gong S, Wang S K, Yu Q H. The growth theorem for biholomorphic mappings in several complex variables. Chin Ann Math, 1993, 14B(1):93-104
[5] Pfaltzgraff J A. Löewner theory in Cⁿ. Abstracts of papers presented to the Amer Math Soc J, 1990, 11:46-63
[6] Zhang W J, Dong D Z. The growth and 1/4 theorem for starlike mappings in a Banach space. Chin Sci Ann, 1991, 18:1371-1372
[7] Chen Z. On the characterization of biholomorphic mappings and starlike mappings in a class of bounded strictly balanced domains in Cⁿ. Chin Ann Math, 1995, 16A(2):230-237
[8] Liu T S, Ren G B. The growth theorem for starlike mappings on bounded starlike circular domains[J]. Chin Ann Math, 1998, 19B:401-408
[9] Feng S X, Liu T S, Ren G B. The growth and covering theorems for several mappings on the unit ball in complex Banach space. Chin Ann Math, 2007, 28A:215-230
[10] Bǎlǎeti C M, Nechita V O. Löewner chains and almost starlike mappings of complex order λ. Carpathian J Math, 2010, 26(2):146-157
[11] Nasr M A, Aouf M K. Starlike function of complex order. J Natur Sci Math, 1985, 25:1-12
[12] Zhao Y H. Almost starlike mappings of complex order λ on the unit ball of a complex Banach space[D]. Zhejiang Normal University, 2013
[13] Löewner K. Untersuchungen über schlichte konforme Abbildungen des Einheitskreises. I Math Ann, 1923, 89:103-121
[14] Kufarev P P. A remark on integrals of the Löewner equation. Dokl Akad Nauk SSSR, 1947, 57:655-656
[15] Pfaltzgraff J A. Subordination chains and univalence of holomorphic mappings in Cⁿ. Math Ann, 1974, 210:55-68
[16] Poreda T. On the univalent subordination chains of holomorphic mappings in Banach spaces. Comment Math, 1989, 28:295-304
[17] Graham I, Hamada H, Kohr G. Parametric representation of univalent mappings in several complex variables. Canad J Math, 2002, 54:324-351
[18] Graham I, Kohr G, Kohr M. Löewner chains and parametric representation in several complex variables. J Math Anal Appl, 2003, 281:425-438
[19] Graham I, Kohr G, Kohr M. Basic properties of Löewner chains in several complex variables//FitzGerald C, Gong S. Geometric Function Theory in Several Complex Variables. River Edge, New Jersey:World Scientific Publishing, 2004:165-181
[20] Abate M, Bracci F, Contreras M, et al. The evolution of Löewner's differential equations. Eur Math Soc Newsl, 2010, 78:31-38
[21] Graham I, Kohr G. Geometric function theory in one and high dimensions. New York:Pure and Applied Math, 2003
[22] Lu J, Liu T S, Wang J F. Distortion theorems for subclasses of starlike mappings along a unit direction in Cⁿ. Acta Mathematica Scientia, 2012, 32B(4):1675-1680
[23] Liu H, Lu K P, Zhang F F. The growth theorem and distortion theorem of spirallike mappings on B_p. Acta Mathematica Sinica (English Series), 2015, 31(5):811-824

GROWTH AND DISTORTION THEOREMS FOR ALMOST STARLIKE MAPPINGS OF COMPLEX ORDER λ

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 6

Metrics

Comments

Recommended 10

[1]	Xiaosong LIU, Taishun LIU. SHARP ESTIMATES OF ALL HOMOGENEOUS EXPANSIONS FOR A SUBCLASS OF QUASI-CONVEX MAPPINGS OF TYPE B AND ORDER α IN SEVERAL COMPLEX VARIABLES [J]. Acta mathematica scientia,Series B, 2016, 36(6): 1804-1818.
[2]	FENG Shu-Xia, LIU Tai-Shun. UNIFORMLY STARLIKE MAPPINGS AND UNIFORMLY CONVEX MAPPINGS ON THE UNIT BALL Bⁿ [J]. Acta mathematica scientia,Series B, 2014, 34(2): 435-443.
[3]	LU Jin, LIU Tai-Shun, WANG Jian-Fei. DISTORTION THEOREMS FOR SUBCLASSES OF STARLIKE MAPPINGS ALONG A UNIT DIRECTION IN Cⁿ [J]. Acta mathematica scientia,Series B, 2012, 32(4): 1675-1680.
[4]	Liu Xiaosong; Liu Taishun. AN INEQUALITY OF HOMOGENEOUS EXPANSION FOR BIHOLOMORPHIC QUASI-CONVEX MAPPINGS ON THE UNIT POLYDISK AND ITS APPLICATION [J]. Acta mathematica scientia,Series B, 2009, 29(1): 201-209.
[5]	Liu Mingsheng; Zhu Yucan. THE EXTENSION OPERATOR IN BANACH SPACES FOR LOCALLY BIHOLOMORPHIC MAPPINGS [J]. Acta mathematica scientia,Series B, 2008, 28(3): 711-720.
[6]	FENG Shu-Xia, LIU Hao. THE GROWTH THEOREM FOR QUASI-CONVEX MAPPINGS IN HILBERT SPACES [J]. Acta mathematica scientia,Series B, 2002, 22(4): 446-450.