The growth theorem and distortion theorem of spirallike mappings on B p

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• 作者：Hao Liu (1)
  Ke Ping Lu (2)
  Fang Fang Zhang (3)
  
  1. School of Mathematics and Statistics ; Institute of Contemporary Mathematics ; He鈥檔an University ; Kaifeng ; 475001 ; P. R. China
  2. College of Mathematics and Information Sciences ; Xinyang Normal University ; Xinyang ; 464000 ; P. R. China
  3. School of Mathematics and Statistics ; He鈥檔an University ; Kaifeng ; 475001 ; P. R. China
  
• 关键词：Parametric representation ; spirallike mappings ; Reinhardt domains ; 30C45 ; 32A30 ; 32H02
• 刊名：Acta Mathematica Sinica
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：31
• 期：5
• 页码：811-824
• 全文大小：240 KB
• 参考文献：1. Ahlfors, V (1966) Complex Analysis. McGraw-Hill, New York
  2. Barnard, R W, FitzGerald, C H, Gong, S (1991) The growth and 1/4 theorems for starlike mapping in 鈩俷. Pacific J. Math. 150: pp. 13-22 CrossRef
  3. Gong, S (1998) Convex and Starlike Mappings in Several Complex Variables. Kluwer Academic Publishers, Netherlands CrossRef
  4. Gong, S (1993) Biholomorphic mappings in several complex variables. Contemp. Math. 142: pp. 15-48 CrossRef
  5. Gurganus, K R (1975) 蠒-like holomorphic functions in 鈩俷 and Banach spaces. Trans. Amer. Math. Soc. 205: pp. 389-406
  6. Jin, F L (1962) Ordinary Differential Equations. Press of Science and Technology of Shang Hai, Shanghai
  7. Liu, T S, Wang, J F, Lu, J (2011) Distortion theorem of starlike mapping in several complex variables. Taiwanese J. Math. 15: pp. 2601-2608
  8. Liu, T S, Ren, G B (1998) The growth theorem for convex mappings on bounded convex circular domains. Sci. China Ser. A 19B: pp. 401-408
  9. Pfaltzgraff, J A (1974) Subordination chains and univalence of holomorphic mappings in 鈩俷. Math. Ann. 210: pp. 55-68 CrossRef
  10. Shi, J H (1996) Foundations of Function Theory in Several Complex Variables. Higher Education Press, Beijing
  11. Suffridge, T J (1976) Starlikeness and convexity and other geometric properties of holomorphic maps in higher dimension.
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, co-published
• ISSN：1439-7617

文摘

In this paper, by using the parametric representation of spirallike mappings, we construct to obtain the growth theorem of spirallike mappings on Reinhardt domain B p . Moreover, the distortion theorem of spirallike mappings is obtained.