多复变数的抛物星形映射

冯淑霞, 张晓飞, 陈慧勇

数学学报 ›› 2011, Vol. 54 ›› Issue (3) : 467-482.

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数学学报 ›› 2011, Vol. 54 ›› Issue (3) : 467-482. DOI: 10.12386/A2011sxxb0048
论文

多复变数的抛物星形映射

    冯淑霞, 张晓飞, 陈慧勇
作者信息 +

Parabolic Starlike Mappings in Several Complex Variables

    Shu Xia FENG, Xiao Fei ZHAGN, Hui Yong CHEN
Author information +
文章历史 +

摘要

本文给出了抛物星形映射, ρ次的抛物星形映射,抛物形β型螺形映射和ρ次的抛物形β型螺形映射的定义.证明了推广的Rope-Suffridge算子保持这些映射的几何性质不变.  

Abstract

We will give the definitions of parabolic starlike mappings, parabolic starlike mappings of order ρ, parabolic and spirallike mappings of type β, parabolic and spirallike mappings of type β and order ρ. Moreover we will prove that the generalized Rope–Suffridge extension operator can preserve these properties.  

关键词

抛物星形映射 / 抛物形β型螺形映射 / 推广的Rope-Suffridge算子

Key words

parabolic starlike mappings / parabolic and spirallike mappings of type β / Rope-Suffridge extension operator

引用本文

导出引用
冯淑霞, 张晓飞, 陈慧勇. 多复变数的抛物星形映射. 数学学报, 2011, 54(3): 467-482 https://doi.org/10.12386/A2011sxxb0048
Shu Xia FENG, Xiao Fei ZHAGN, Hui Yong CHEN. Parabolic Starlike Mappings in Several Complex Variables. Acta Mathematica Sinica, Chinese Series, 2011, 54(3): 467-482 https://doi.org/10.12386/A2011sxxb0048

参考文献

[1] Cartan H., Sur la possibilit′e d’′etendre aux fonctions de plusieurs variables complexes la theorie des fonctionsunivalents, Lecons sur les Fonctions Univalents ou Mutivalents, by P. Montel, Paris: Gauthier-Villars, 1933:129-155.



[2] Gong S., Convex and Starlike Mappings in Several Complex Variables (II), Beijing: Science Press Company,2003 (in Chinese).



[3] Graham I., Kohr G., Geometric Function Theory in one and Higher Dimensions, New York: Marcel Dekker,2003.



[4] Suffridge T. J., Starlikeness, convexity and other geometric properties of holomorphic maps in higher dimensions,Complex Analysis, Kentucky, 1977, 599: 146-159.



[5] Gong S., The Bieberbach Conjecture, Company: International Press Company, 1999.



[6] Roper K. A., Suffridge T. J., Convexity properties of holomorphic mappings in Cn, Tran. Amer. Soc., 1999,351(5): 1803-1833.



[7] Liu T. S., Liu H., Quasi-convex mappings on bounded convex circular domains, Acta Math. Sci., 2001, 44(2):287-292 (in Chinese).



[8] Liu T. S., Zhang W. J., The growth and covering theorem of quasi-convex mappings in complex Banach spase,Science in China A, 2002, 32(11): 1033-1041 (in Chinese).



[9] Feng S. X., Liu T. S., Ren G. B., The growth and covering theorems for several mappings on the unit ball incomplex Banach space, Chin. Ann. of Math., 2007, 28(A): 215-230 (in Chinese).



[10] Rønning F., Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math.Soc., 1993, 118: 189-196.



[11] Rønning F., On starlike functions associated with parabolic regions, Ann. Univ. Mariae Curie Sklodowska,1991, 45: 117-122.



[12] Ali R. M., Starlikeness associated with parabolic regions, Int. J. Math. Sci., 2005, 4: 561-570.



[13] Roper K. A., Suffridge T. J., Convex mappings on the unit ball of Cn, Anal. Math., 1995, 65: 333-347.



[14] Graham I., Kohr G., Univalent mappings associated with the Roper-Suffridge extension operator, AnalyseMath., 2000, 81: 331-342.



[15] Graham I., Kohr G., Kohr M., Loewner chains and Roper-Suffridge extension operator, J. Math. Anal.Appl., 2000, 247: 448-465.



[16] Pfaltzgraff J. A., Suffridge T. J., An extension theorem and linear invariant families generated by starlikemaps, Ann. Univ. Mariae Curie Sklodowsda, 1999, 53(A): 193-207.



[17] Graham I., Hamada H., Kohr G., Suffridge T. J., Extension operators for locally univalent mappings, MichiganMath., 2002, 50: 37-55.



[18] Feng S. X., Liu T. S., The generalized Roper-Suffridge extension operator, Acta Math. Sci., 2008, 28(B):63-80.



[19] Feng S. X., Yan C. Y., Hong J., Property of generalized Roper-Suffridge extension operator on Reinhardtdomains and the unit ball in complex Hilbert spaces, J. of Henan University (Natural Science), 2008, 38(1):1-7 (in Chinese).



[20] Zhu Y. C., Liu M. S., The generalized Roper-Suffridge extension operator on bounded complete Reinhardtdomains, Science in China A, 2007, 50(12): 1781-1794.



[21] Liu X. S., Liu T. S., The generalized Roper-Suffridge extension operator on a Reinhardt domain and theunit ball in a complex Hilbert space, Chin. Ann. of Math., 2005, 26A(5): 721-730 (in Chinese).



[22] Liu T. S., Zhang W. J., On decomposition theorem of normalized biholomorphic convex mappings in Reinhardtdomains, Science in China A, 2003, 46(1): 94-106.

基金

国家自然科学基金资助项目(11001074,11061015), 河南省高等学校青年骨干教师资助计划项目

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