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
.
DOI: 10.1016/S0252-9602(18)30782-3
[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 Bp. Acta Mathematica Sinica (English Series), 2015, 31(5):811-824