Roper-Suffridge延拓算子与Loewner链

Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (3): 433-440.

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Generalized Roper-Suffridge Extension Operators and Loewner Chains

Wang Chaojun¹, Cui Yanyan¹, Liu Hao²

1 College of Mathematics and Statistics, Zhoukou Normal University, Henan Zhoukou 466001;
2 College of Mathematics and Information Science, Henan University, Kaifeng 475001

Received:2015-12-13 Revised:2016-03-29 Online:2016-06-26 Published:2016-06-26
Supported by:
Supported by the NSFC (U1204618), the Natural Science Foundation of Henan Province (2011B110034) and the Key Project of Science and Technology Research of Henan Provincial Department of Education (14B110015, 14B110016)

Abstract

Abstract:

In this paper, we mainly seek conditions under which a kind of generalized Roper-Suffridge operators can be embedded in Loewner chains. Sequentially, by the analytical characteristics of almost spirallikeness of order α and type β, we discuss the generalized Roper-Suffridge operators preserve almost spirallikeness of order α and type β on a bounded and completely Reinhardt domain. The conclusions generalize the previous results.

Key words: Roper-Suffridge operators, Almost spirallike mappings of type β and order α, Loewner Chains

CLC Number:

O174.56

Wang Chaojun, Cui Yanyan, Liu Hao. Generalized Roper-Suffridge Extension Operators and Loewner Chains[J].Acta mathematica scientia,Series A, 2016, 36(3): 433-440.

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References

[1] Graham I, Kohr G. Univalent mappings associated with the Roper-Suffridge extension operator. J Analyse Math, 2000, 81(1):331-342
[2] Muir J R. A modification of the Roper-Suffridge extension operator. Comput Methods Funct Theory, 2005, 5(1):237-251
[3] Feng S X, Liu T S. The generalized Roper-Suffridge extension operator. Acta Math Sci, 2008, 28B:63-80
[4] Hamada H, Kohr G. Subordination chains and the growth theorem of spirallike mappings. Mathematica (Cluj), 2000, 42(65):153-161
[5] Kohr G. Using the method of Loewner chains to introduce some subclasses of biholomorphic mappings in Cⁿ. Rev Roum Math Pures Appl, 2001, 46:743-760
[6] Graham I, Kohr G, Kohr M. Loewner chains and the Roper-Suffridge extension operator. J Math Anal Appl, 2000, 247:448-465
[7] Liu T S, Xu Q H. Loewner chains associated with the Roper-Suffridge extension operator. J Math Anal Appl, 2006, 322:107-120
[8] Feng S X, Liu X S, Xu Q H. Loewner chains and the generalized Roper-Suffridge extension operator. Acta Mathematica Scientia, 2009, 29A(6):1601-1612
[9] Poreda T. On the univalent subordination chains of holomorphic mappings in Banach spaces. Commentationes Math, 1989, 28:295-304
[10] Pommerenke C. Über die subordination analytischer Funktion. J Reine Angew Math, 1965, 218:159-173
[11] Graham I, Kohr G. Geometric Function Theory in One and Higher Dimensions. New York:Marcel Dekker, 2003
[12] Liu M S, Zhu Y C. The generalized Roper-Suffridge extension operator on bounded completiy Reinhardt domains. Science in China, 2007, 37(10):1193-1206
[13] Muir J R. A class of Loewner chain preserving extension operators. J Math Anal Appl, 2008, 337(2):862-879
[14] 崔艳艳, 王朝君. Reinhardt域上推广的Roper-Suffridge算子与Lowner链. 中北大学学报(自然科学版), 2014, 35(4):376-393 Cui Y Y, Wang C J. The generalized Roper-Suffridge extension operator on Reinhardt domains and Lowner chains. J North Univ China (Natural Science Edition), 2014, 35(4):376-393

Generalized Roper-Suffridge Extension Operators and Loewner Chains

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